Question

if X square + 1 by x square is equals to 51 then find the value of x cube minus 1 by x cube

Answer 1

You answer is here........
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Answer 2

Answer:

The value of required expression is 364.

Step-by-step explanation:

We are given $x^2+\frac{1}{x^2}=51$

To find: Value of  $x^3-\frac{1}{x^3}$

we know that ,

( a - b )² = a² + b² - 2ab

take a = x and b =  $\frac{1}{x}$

we get,

$(x-\frac{1}{x})^2=x^2+(\frac{1}{x})^2-2\timesx\times\frac{1}{x}$

$(x-\frac{1}{x})^2=x^2+\frac{1}{x^2}-2$

$(x-\frac{1}{x})^2=51-2$

$x-\frac{1}{x}=\sqrt{49}$

$x-\frac{1}{x}=7$

Also, we know that

( a - b )³ = a³ - b³ - 3ab( a - b )

take a = x and b = $\frac{1}{x}$

$(x-\frac{1}{x})^3=x^3-\frac{1}{x^3}-3\timesx\times\frac{1}{x}(x-\frac{1}{x})$

$(7)^3=x^3-\frac{1}{x^3}-3\times(7)$

$x^3-\frac{1}{x^3}=343+21$

$x^3-\frac{1}{x^3}=364$

Therefore, The value of required expression is 364.