Question

√(2x-6) + √(x+4) =5. Pls solve this question with detailed steps!!

Answer 1

Square both sides:

(2x - 6) + (x + 4) + 2 sqrt ((2x - 6)(x + 4)) = 25

Then isolate the remaining sqrt term:

2 sqrt ((2x - 6)(x + 4) = 27 - 3x

Then square both sides:

4 (2x - 6)(x + 4) = 729 - 162x + 9x²

Expand:

8x² + 8x - 96 = 729 - 162x + 9x²

Put all on one side:

x² - 170x + 825 = 0

Solve by quadratic formula or otherwise:

x = (170 +/- sqrt (170² - 3300)) / 2

= (170 +/- 160) / 2

= 5 or 165.

But for some reason 165 doesn't work, so x = 5.
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Answer 2

√(2x - 6) + √( x + 4) = 5

√{2( x +4) -14} + √(x +4) = 5

let ( x +4) = Q

√{2Q -14) + √Q = 5

√(2Q -14) = 5 - √Q

take square both sides

2Q - 14 = 25 + Q -10√Q

Q -39 = -10√Q

Q + 10√Q -39 = 0

√Q = t

t² + 10t -39 = 0

t² +13t -3t -39 = 0

( t + 13)( t -3) = 0

t = -13 , 3

but t > 0 becoz t = √Q
so,
t = √Q = 3

Q = 9

x + 4 = 9

x = 5