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

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Answer 1 · 2018-06-22T15:57:08

$x = 3$ $x=3$

Squaring the given equation

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

$\sqrt{2 x - 2} \sqrt{7 x + 4} = 2 x + 4$ $sqrt(2x-2)sqrt(7x+4)=2x+4$

squaring again and simplifying we get

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

$x_{1} = 3$ $x_1=3$
$x_{2} = - \frac{4}{5}$ $x_2=-4/5$ which is not a solution!

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