Answer:
Here!!
Step-by-step explanation:
Here are a few ratios that are equivalent to 4 : 11 . . . . .
8 : 22
12 : 33
20 : 55
400 : 1100
308 : 847
4 billion : 11 billion
I like the first one and tje third one
a = 6, is your answer.
Square both sides
<span><span><span>9=a−2<span>(6−a)(2a−3)</span>+3</span>9=a-2\sqrt{(6-a)(2a-3)}+3</span><span>9=a−2<span>√<span><span><span>(6−a)(2a−3)</span></span><span></span></span></span>+3
</span></span>2 .Separate terms with roots from terms without roots
<span><span><span>9−a−3=−2<span>(6−a)(2a−3)</span></span>9-a-3=-2\sqrt{(6-a)(2a-3)}</span><span>9−a−3=−2<span>√<span><span><span>(6−a)(2a−3)
</span></span><span></span></span></span></span></span>
3. Simplify <span><span><span>9−a−3</span>9-a-3</span><span>9−a−3</span></span> to <span><span><span>6−a</span>6-a</span><span>6−a
</span></span><span><span><span>6−a=−2<span>(6−a)(2a−3)</span></span>6-a=-2\sqrt{(6-a)(2a-3)}</span><span>6−a=−2<span>√<span><span><span>(6−a)(2a−3)
</span></span><span></span></span></span></span></span>
4 .Square both sides
<span><span><span><span><span>(6−a)</span>2</span>=4(6−a)(2a−3)</span>{(6-a)}^{2}=4(6-a)(2a-3)</span><span><span><span>(6−a)</span><span><span>2</span><span></span></span></span>=4(6−a)(2a−3)
</span></span>5 .Expand
<span><span><span>36−12a+<span>a2</span>=48a−72−8<span>a2</span>+12a</span>36-12a+{a}^{2}=48a-72-8{a}^{2}+12a</span><span>36−12a+<span>a<span><span>2</span><span></span></span></span>=48a−72−8<span>a<span><span>2</span><span></span></span></span>+12a
</span></span>6. Simplify <span><span><span>48a−72−8<span>a2</span>+12a</span>48a-72-8{a}^{2}+12a</span><span>48a−72−8<span>a<span><span>2</span><span></span></span></span>+12a</span></span> to <span><span><span>60a−72−8<span>a2</span></span>60a-72-8{a}^{2}</span><span>60a−72−8<span>a<span><span>2</span><span></span></span></span></span></span>
<span><span><span>36−12a+<span>a2</span>=60a−72−8<span>a2</span></span>36-12a+{a}^{2}=60a-72-8{a}^{2}</span><span>36−12a+<span>a<span><span>2</span><span></span></span></span>=60a−72−8<span>a<span><span>2
</span><span></span></span></span></span></span>
7. Move all terms to one side
<span><span><span>36−12a+<span>a2</span>−60a+72+8<span>a2</span>=0</span>36-12a+{a}^{2}-60a+72+8{a}^{2}=0</span><span>36−12a+<span>a<span><span>2</span><span></span></span></span>−60a+72+8<span>a<span><span>2</span><span></span></span></span>=0
</span></span>8. Simplify <span><span><span>36−12a+<span>a2</span>−60a+72+8<span>a2</span></span>36-12a+{a}^{2}-60a+72+8{a}^{2}</span><span>36−12a+<span>a<span><span>2</span><span></span></span></span>−60a+72+8<span>a<span><span>2</span><span></span></span></span></span></span> to <span><span><span>36−72a+9<span>a2</span>+72</span>36-72a+9{a}^{2}+72</span><span>36−72a+9<span>a<span><span>2</span><span></span></span></span>+72</span></span>
<span><span><span>36−72a+9<span>a2</span>+72=0</span>36-72a+9{a}^{2}+72=0</span><span>36−72a+9<span>a<span><span>2</span><span></span></span></span>+72=0
</span></span>9 .Simplify <span><span><span>36−72a+9<span>a2</span>+72</span>36-72a+9{a}^{2}+72</span><span>36−72a+9<span>a<span><span>2</span><span></span></span></span>+72</span></span> to <span><span><span>−72a+9<span>a2</span>+108</span>-72a+9{a}^{2}+108</span><span>−72a+9<span>a<span><span>2</span><span></span></span></span>+108</span></span>
<span><span><span>−72a+9<span>a2</span>+108=0</span>-72a+9{a}^{2}+108=0</span><span>−72a+9<span>a<span><span>2</span><span></span></span></span>+108=0
</span></span>10.Factor out the common term <span><span>99</span>9</span>
<span><span><span>−9(8a−<span>a2</span>−12)=0</span>-9(8a-{a}^{2}-12)=0</span><span>−9(8a−<span>a<span><span>2</span><span></span></span></span>−12)=0
</span></span>11. Factor out the negative sign
<span><span><span>−9×−(<span>a2</span>−8a+12)=0</span>-9\times -({a}^{2}-8a+12)=0</span><span>−9×−(<span>a<span><span>2</span><span></span></span></span>−8a+12)=0
</span></span>12. Divide both sides by <span><span><span>−9</span>-9</span><span>−9</span></span>
<span><span><span>−<span>a2</span>+8a−12=0</span>-{a}^{2}+8a-12=0</span><span>−<span>a<span><span>2</span><span></span></span></span>+8a−12=0
</span></span>13. Multiply both sides by <span><span><span>−1</span>-1</span><span>−1</span></span>
<span><span><span><span>a2</span>−8a+12=0</span>{a}^{2}-8a+12=0</span><span><span>a<span><span>2</span><span></span></span></span>−8a+12=0
</span></span>14. Factor <span><span><span><span>a2</span>−8a+12</span>{a}^{2}-8a+12</span><span><span>a<span><span>2</span><span></span></span></span>−8a+12</span></span>
<span><span><span>(a−6)(a−2)=0</span>(a-6)(a-2)=0</span><span>(a−6)(a−2)=0
</span></span>15. Solve for <span><span>aa</span>a</span>
<span><span><span>a=6,2</span>a=6,2</span><span>a=6,2
</span></span>16 Check solution
When <span><span><span>a=2</span>a=2</span><span>a=2</span></span>, the original equation <span><span><span>−3=<span>6−a</span>−<span>2a−3</span></span>-3=\sqrt{6-a}-\sqrt{2a-3}</span><span>−3=<span>√<span><span><span>6−a</span></span><span></span></span></span>−<span>√<span><span><span>2a−3</span></span><span></span></span></span></span></span> does not hold true.
We will drop <span><span><span>a=2</span>a=2</span><span>a=2</span></span> from the solution set.
17. Therefore,
<span><span><span>a=6</span></span><span /></span>
