Solve the following equations for x and y: 1. sqrt(y - 4)  = x + 12. sqrt(y + 4) = x + 2

Expert Answers

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We have the following equations to solve for y.

sqrt ( y - 4) = x + 1

=> y - 4 = x^2 + 2x + 1...(1)

sqrt ( y - 4) = x + 2

=> y + 4 = x^2 + 4x + 4...(2)

from (1) - (2) , we get

y - 4 - y - 4 = x^2 + 2x + 1 - x^2 - 4x - 4

=> -8 = -2x - 3

=> 2x = 5

=> x = 5/2

substituting this in (1)

y - 4 = (5/2)^2 + 2*(5/2) + 1

=> y = (5/2)^2 + 5 + 1 + 4

=> y = 25/4 + 10

=> y = 65/4

Therefore x is 5/2 and y is 65/4.

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