# Math Help - Equation needed to be solve for X

1. ## Equation needed to be solve for X

If (square root of 4+x) + (square root of 10-x) = 6.
Then solve (square root (4+x)(10-x)).

(4+x)^(1/2) + (10-x)^(1/2) = 6.
Then solve (4+x)(10-x)^(1/2)

2. Originally Posted by crystaly0x
If (square root of 4+x) + (square root of 10-x) = 6.
Then solve (square root (4+x)(10-x)).

(4+x)^(1/2) + (10-x)^(1/2) = 6.
Then solve (4+x)(10-x)^(1/2)
Let $\sqrt{4 + x} = a$
$\sqrt{10 - x} = b$
Therefore,
a + b = 6
$(a + b)^2 = 36$
$a^2 + 2ab + b^2 = 36$
$2ab = 36 - a^2 - b^2$
$2ab = 36 - (\sqrt{4 + x})^2 - (\sqrt{10-x})^2$
2ab = 36 - (4 + x) - (10 - x)
2ab = 22
ab = 11
hence $\sqrt{4 + x}\sqrt{10 - x} = \sqrt{(4 + x)(10 - x)}$ = 11