<span>Step 1: 0.06 = 6⁄100</span>
<span>Step 2: Simplify 6⁄100 = 3⁄50</span><span>
hope this helps:)
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Answer:
- 4x² - 13x + 8 = 0
- 4x² - 11x + 5 = 0
- 16x² - 41x + 1 = 0
- x² + 5x + 4 = 0
- x² - 66x + 64 = 0
Step-by-step explanation:
<u>Given</u>
- α and β are roots of 4x²-5x-1=0
<u>Then the sum and product of the roots are:</u>
- α+b = -(-5)/4 = 5/4
- αβ = -1/4
(i) <u>Roots are α + 1 and β + 1, then we have:</u>
- (x - (α + 1))(x - (β + 1)) = 0
- (x - α - 1)(x - β - 1) = 0
- x² - (α+β+2)x + α+β+ αβ + 1 = 0
- x² - (5/4+2)x +5/4 - 1/4 + 1 = 0
- x² - 13/4x + 2= 0
- 4x² - 13x + 8 = 0
(ii) <u>Roots are 2 - α and 2 - β, then we have:</u>
- (x + α - 2)(x + β - 2) = 0
- x² + (a + β - 4)x - 2(α + β) + αβ + 4 = 0
- x² + (5/4 - 4)x - 2(5/4) - 1/4 + 4 = 0
- x² - 11/4x - 10/4 - 1/4 + 16/4 = 0
- x² - 11/4x + 5/4x = 0
- 4x² - 11x + 5 = 0
(iii) <u>Roots are α² and β², then:</u>
- (x - α²)(x-β²) = 0
- x² -(α²+β²)x + (αβ)² = 0
- x² - ((α+β)² - 2αβ)x + (-1/4)² = 0
- x² - ((5/4)² -2(-1/4))x + 1/16 = 0
- x² - ( 25/16 + 1/2)x + 1/16 = 0
- x² - 33/16x + 1/16 = 0
- 16x² - 33x + 1 = 0
(iv) <u>Roots are 1/α and 1/β, then:</u>
- (x - 1/α)(x - 1/β) = 0
- x² - (1/α+1/β)x + 1/αβ = 0
- x² - ((α+β)/αβ)x + 1/αβ = 0
- x² - (5/4)/(-1/4)x - 1/(-1/4) = 0
- x² + 5x + 4 = 0
(v) <u>Roots are 2/α² and 2/β², then:</u>
- (x - 2/α²)(x - 2/β²) = 0
- x² - (2/α² + 2/β²)x + 4/(αβ)² = 0
- x² - 2((α+β)² - 2αβ)/(αβ)²)x + 4/(αβ)² = 0
- x² - 2((5/4)² - 2(-1/4))/(-1/4)²x + 4/(-1/4)² = 0
- x² - 2(25/16 + 8/16)/(1/16)x + 4(16) = 0
- x² - 2(33)x + 64 = 0
- x² - 66x + 64 = 0
Answer:
x > 3
Step-by-step explanation:
-2(x-5) < 4
-2x+10 < 4
-2x < -6
x > 3
Answer:
x=49
Step-by-step explanation:
2(3x+1)=3(2−x)
Step 1: Simplify both sides of the equation.
2(3x+1)=3(2−x)
(2)(3x)+(2)(1)=(3)(2)+(3)(−x)(Distribute)
6x+2=6+−3x
6x+2=−3x+6
Step 2: Add 3x to both sides.
6x+2+3x=−3x+6+3x
9x+2=6
Step 3: Subtract 2 from both sides.
9x+2−2=6−2
9x=4
Step 4: Divide both sides by 9.
9x9=49
x=49
