How do you solve $sqrt( 2x - 2 ) + sqrt( 7x + 4 ) = sqrt( 13x + 10)$ ?

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Answer 1 · 2018-06-22T15:57:08

$x=3$

Squaring the given equation

$2x-2+7x+4+2sqrt(2x-2)sqrt(7x+4)=13x+10$

$sqrt(2x-2)sqrt(7x+4)=2x+4$

squaring again and simplifying we get

$x^2-11/5x-12/5=0$
solving this equation we get

$x_1=3$
$x_2=-4/5$ which is not a solution!

How do you solve sqrt( 2x - 2 ) + sqrt( 7x + 4 ) = sqrt( 13x + 10)sqrt( 2x - 2 ) + sqrt( 7x + 4 ) = sqrt( 13x + 10)?