x = 5 is not an extraneous solution of the equation.
✓(2x + 6) - ✓(x - 1) = 2
✓(2x + 6) = 2 + ✓(x - 1)
Squaring both the sides of equation, we get
(✓(2x + 6))² = (2 + ✓(x - 1))²
2x + 6 = (2)² + (✓(x - 1))² + 2(2)(✓(x - 1))
2x + 6 = 4 + x - 1 + 4(✓(x - 1))
x + 3 = 4✓(x - 1)
Squaring again on both the side of the equation, we get
(x + 3)² = (4✓(x - 1))²
x² + 3² + 2×3×x = 16(x - 1)
x² + 9 + 6x = 16x - 16
x² - 10x + 25 = 0
By applying middle term splitting on equation (1), we get
x² - 5x - 5x + 25 = 0
x(x - 5) -5(x - 5) = 0
(x - 5) (x - 5) = 0
x = 5 and 5.
Check for extraneous solutions by putting value of x in original equation -
✓(2×5 + 6) - ✓(5 - 1) = 2
✓16 - ✓4 = 2
4 - 2 = 2
2 = 2
LHS = RHS
x = 5 is not an extraneous solution of the equation.
Know more about roots of equation -
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So the other equation is
2.5 times as many kilos of rasins than sunflower seeds or
rasin kilos=2.5 times sunflower seed kilos
r=2.5s
the 2 equations are
12s+6r=108 and
r=2.5s
you can simplify the first equation (that sometimes helps)
undistribute the 6 from both left side
6(2s+r)=108
divide both sides by 6
2s+r=18
now use r=2.5s and subsitute 2.5s for r in first equation
2s+2.5s=18
4.5s=18
divide both sides by 4.5
s=4
subsitute
r=2.5 times s
s=4
r=2.5 times 4
r=10
rasins=10 kilos
sunflower seeds=4 kilos
Answer:Point Form:
(2,0)
Equation Form:
x=2,y=0
Step-by-step explanation:Add the equations in order to solve for the first variable. Plug this value into the other equations in order to solve for the remaining variables.
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