Find the root(s) of the equation $y+\sqrt{y+5}=7$
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11
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4
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4 and 11
- $\pm 4$
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none of these
Reveal answer
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B
Correct answer
Explanation
y + sqrt(y+5) = 7 => sqrt(y+5) = 7-y. Square both sides: y+5 = 49 - 14y + y^2 => y^2 - 15y + 44 = 0. Factors: (y-11)(y-4) = 0. y=11 (extraneous, 11+sqrt(16)=15!=7) or y=4 (4+sqrt(9)=7).
AI explanation
Isolate the radical to get the square root of (y + 5) = 7 - y. Squaring both sides yields y + 5 = 49 - 14y + y^2, which rearranges to the quadratic equation y^2 - 15y + 44 = 0. Factoring this gives (y - 4)(y - 11) = 0, so the potential roots are 4 and 11. Substituting y = 11 into the original equation fails because 11 plus the square root of 16 is not 7, but substituting y = 4 works. The only valid root is 4.