Question

Value of x satisfying under root x + 3 + under root x - 2 =5

Answer 1

Answer:

x=under root 2

Step-by-step explanation:

as 5+2 will be 7and 7-3 will be 4 and the those two under root that two will be divided by 4 and it will be 2 now

under root x=2

when under root will go this side it will be under root 2 ans

Answer 2

Given:

under root( x + 3 )+ under root (x - 2) =5

To Find:

Value of x

Solution:

let's start by writing down the equation which is,

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

Squaring both sides of the equation trying to eliminate the root part, we have

$(\sqrt{x+3} +\sqrt{x-2})^2 =5^2\\x+3+x-2+2\sqrt{(x+3)(x-2)} =25\\2x+1+2\sqrt{(x+3)(x-2)} =25$

Now taking the root equation to the left side and the others on right and then again squaring both sides we have,

$2x+1+2\sqrt{(x+3)(x-2)} =25\\\\2\sqrt{(x+3)(x-2)}=24-2x\\\sqrt{(x+3)(x-2)}=12-x$

Now squaring both sides we have,

$(\sqrt{(x+3)(x-2)})^2=(12-x)^2\\\\(x+3)(x-2)=144+x^2-24x\\x^2+x-6=144+x^2-24x\\25x=150\\x=6$

Hence, the value of x is 6.