Question

find the value of x √x+3 +√x—2 =5​

Answer 1

Answer:       $x=6$

Step-by-step explanation:

Alright, lets get started.

The given equation is:

$\sqrt{x+3}+\sqrt{x-2}=5$

Squaring both sides

Using the formula : $(a+b)^2=a^2 + b^2 + 2ab$

So,

$(x+3)+ (x-2)+ 2\sqrt{x+3} \sqrt{x-2}=25$

$2x+1+2\sqrt{x+3} \sqrt{x-2}=25$

$2x+2\sqrt{x+3} \sqrt{x-2}=24$

$x+\sqrt{x+3} \sqrt{x-2}=12$

$\sqrt{x+3} \sqrt{x-2}=(12-x)$

Squaring on both sides once again

$(x+3)(x-2)=144+x^2-24x$

$x^2-2x+3x-6=144+x^2-24x$

taking similar terms together

$25x=150$

$x=6$   ................   Answer

Hope it will help :)