Question

solve for

√2x+9 + x = 13

Answer 1

$\huge\mathcal{Heya!!}$

Given :-

√2x + 9 + x = 13

√2x + x = 13 - 9

√2x + x = 4

x (√2 + 1) = 4

$x = \frac{4}{ \sqrt{2} + 1}$

On rationlising the denominator, we get

$x = \frac{4}{ \sqrt{2} + 1} \times \frac{ \sqrt{2} - 1}{ \sqrt{2} - 1} \\ \\ x = \frac{4( \sqrt{2} - 1)}{ ({ \sqrt{2} )}^{2} - {(1)}^{2} } \\ \\ x = \frac{4( \sqrt{2} - 1)}{2 - 1} \\ \\ x = 4 \sqrt{2} - 4$


$\huge\mathbb{Hope \ this \ helps.}$

Answer 2

√2x+ 9 + x = 13


√ 2x+ 9 = 13-x

(√ 2x+ 9 )^2 = (13-x)^2

both side square

2x+9= 169+x^2-26x


x^2 -26x -2x +169-9=0

x^2-28x +160=0

x^2-20x -8x +160 =0

x(x-20)-8(x-20)=0

(x-20)(x-8) =0

x-20=0 or x=8

but x= 20 does not satisfied the equation.


I hope help you