Question

If x-2/x=3, find the value of x cube -8/x
​

Answer 1

Solution

Given That:-

• x - 2/x = 3 ----------(1)

Find :-

• Value of ( x³ - 8/x³ )

Explanation

Important Formula

☛ (a+b)² = (a² + b² + 2ab)

☛(a³ - b³) = (a-b)(a²+b²+ab)

So, Squaring both sides of equ(1)

➥ ( x - 2/x)² = 3²

➥ x² + (2/x)² - 2 * x * 2/x = 9

➥ x² + 4/x² = 9 + 4

➥ x² + 4/x² = 13 --------------(2)

So, Now Calculate Value of ( x³ - 8/x³ )

➥ ( x³ - 8/x³ ) = ( x - 2/x)(x² + 4/x² - x * 2/x)

➥ ( x³ - 8/x³ ) = ( x - 2/x)(x² + 4/x² - 2)

Keep Value by equ(1) & equ(2)

➥ ( x³ - 8/x³ ) = 3 * ( 13 - 2)

➥ ( x³ - 8/x³ ) = 3 * 11

➥ ( x³ - 8/x³ ) = 33

Hence

• Value of ( x³ - 8/x³ ) = 33

___________________

Answer 2

* Answer=33 *

$\rule{300}2$

◇ Correct Question ◇

* if $\large\frac{x-2}{x=3},$ find the value of $x^2\frqc{-8}{x}$.

† Given †

→$\large\frac{x-2}{x=3}$-------eq(1)

→$\rule{300}2$

* To find *

→$\large x^3\frac{-8}{x}$.

★ Solution ★

→ Squaring both side on $\large\frac{x-2}{x=3}$

* we get *

$\rightarrow \large(x-2/x)^2=3^{2} \\ \rightarrow x^{2}+(2/x)^{2}-2×x×2/x=9 \\ \rightarrow x^{2}+4/x^{2}=13$ ------eq(2)

so,

$\rightarrow\large x^3\frac{-8}{x}$.

$\rightarrow \large x^3\frac{-8}{x}= (x-2/x)(x^{2}+4/x^{2}-x×2/x) \\ \rightarrow x^3\frac{-8}{x} = (x-2/x)(x^{2}+4/x^{2}-2)$

Putting value in equation (1) and (2)--

$\rightarrow \large x^3\frac{-8}{x} = 3×(13-2) \\\rightarrow x^3\frac{-8}{x}=33 Answer$

$\rule{300}2$