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Mathematics
Sandra Lara
23 October, 21:49
Solve by Extraneous : sqrt x+7-x=1
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Darien Cole
23 October, 23:50
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√ (x+7) - x=1
√ (x+7) = x+1
[√ (x+7) ]² = (x+1) ²
x+7=x²+2x+1
x²+x-6=0
x=[-1⁺₋√ (1+24) ]/2 = (-1⁺₋5) / 2
We have two possible solutions:
x₁ = (-1-5) / 2=-6/2=-3
x₂ = (-1+5) / 2=4/2=2
We must check the answer:
if x₁=-3 ⇒√ (x+7) - x=√4 + 3=2+3=5≠1; then x₁=-3 is not a solution for this equation.
if x₂=2; ⇒√ (x+7) - x=√9-2=3-2=1; then x₂=2 is a solution for this equation.
answer: the only one solution is x=2;
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