Question

Solve the following equations;-

x - 9 /√x + 3 =1

Answer 1

13 , 6.

Explanation:

A equation is given to us and we need to find out the value of x . The given equation to us is ,

`\sf\implies ( x -9)/(√(x+3))= 1`

Cross multiply ,

`\sf\implies x - 9 =√( x +3)`

Squaring both sides ,

`\sf\implies (x - 9)^2 = x + 3`

Simplify the whole square ,

`\sf\implies x^2+9^2-2.9.x = x +3 \\`

`\sf\implies x^2+81 - 18x = x -3`

Add 3 and subtract x on both sides ,

`\sf\implies x^2 -18x-x +81-3=0`

Simplify ,

`\sf\implies x^2 -19x +78=0`

Split the middle term of the quadratic equation,

`\sf\implies x^2-13x-6x+78=0`

Take out common ,

`\sf\implies x( x -13)-6(x-13)=0`

Take out ( x -13 ) as common ,

`\sf\implies ( x -13)(x-6)=0`

Equate both factors to 0 ,

`\sf\implies \boxed{\pink{\sf x = 13,6}}`

Hence the value of x is 13 or 6 .