How do you solve $4 sqrt (x) = 8 + 2 sqrt (x)$ ?

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Answer 1 · 2015-09-13T08:42:42

$color(green)(x = 16$

We are given that $4 sqrt (x) = 8 + 2 sqrt (x)$

Transposing $2sqrtx$ to the left hand side, we get:

$4 sqrt (x) - 2 sqrt (x) = 8$

$(4-2)sqrtx = 8$

$2sqrtx = 8$

Divising both sides by 2, we get:

$(cancel(2)sqrtx)/cancel(2) = 8/2$

$sqrtx = 4$

Squaring both sides we get:

$(sqrtx)^2 = 4^2$

In exponents, $color(blue)(sqrta*sqrta = a$

Hence we get $color(green)(x = 16$

How do you solve 4 sqrt (x) = 8 + 2 sqrt (x)4 sqrt (x) = 8 + 2 sqrt (x)?