Question

if x + 9/x = 6 then x² = ?
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Answer 1

GIVEN:-

• $\rm{ x + \dfrac{9}{x} = 6}$

TO FIND:-

• x²

Now,

$\implies\rm{ x + \dfrac{9}{x} = 6}$

$\implies\rm{ \dfrac{x^2 + 9}{x} = 6}$

$\implies\rm{ x^2 + 9 = 6x}$

$\implies\rm{ x^2 + 9 - 6x}$.

$\implies\rm{ x^2 -6x + 9}$

$\implies\rm{ x^2 -3x - 3x + 9 = 0}$

$\implies\rm{ x(x-3) -3(x-3) = 0}$

$\implies\rm{ x = 3}$

Therefore,

$\to{ x^2 = (3)^2}$

$\to{ x^2 =9}$.

Hence, The Value of x² is 9.

SOME ALGEBRAIC IDENTITIES

• $\rm{ (a+b)^2 = a^2 + 2ab + b^2 }$

• $\rm{ (a-b)^2 = a^2 - 2ab + b^2 }$

• $\rm{ (a+b)^3 = a^3 + b^3 + 3a^2b + 3ab^2 }$

• $\rm{(a-b)^3 = a^3 - b^3 +3a^2b -3ab^2 }$

Answer 2

x + 9/ x. = 6

x + 9 = 6x

5x = 9

x = 9/5

x² + 9 /x²

81/25 + 9 / 81/25

= 81 + 225/25/81/25

= 1 + 9 .

= 10

hope it helps you