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zzz [600]
2 years ago
10

Solve the following equations;- x - 9 /√x + 3 =1

Mathematics
1 answer:
fgiga [73]2 years ago
7 0

Answer:

13 , 6.

Step-by-step 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 \dfrac{ x -9}{\sqrt{x+3}}= 1

Cross multiply ,

\sf\implies x - 9 =\sqrt{ 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}}

<u>Hence</u><u> the</u><u> </u><u>value</u><u> of</u><u> </u><u>x</u><u> is</u><u> </u><u>1</u><u>3</u><u> </u><u>or </u><u>6</u><u> </u><u>.</u>

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