Question

If y-1/y=6 find the value of y^3-1/y^3​

Answer 1

Answer:

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Answer 2

Concept: Finding the value of an algebraic expression when a specified integer is used to replace a variable is known as evaluating the expression. We use the provided number to replace the expression's variable before applying the sequence of operations to simplify the expression.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. We have LHS = RHS (left hand side = right hand side) in every mathematical equation. To determine the value of an unknown variable that represents an unknown quantity, equations can be solved.

Given: $y-\dfrac1y=6$

Find: $y^3-\dfrac{1}{y^3}$

Solution:

We have

$y-\dfrac{1}{y}=6$

So,

$\left(y-\dfrac 1 y \right)^2=y^2-2+\dfrac 1 {y^2}$

$\implies y^2+\frac 1 {y^2} = 6^2+2=36+2=38$

So,$y^3-\dfrac{1}{y^3}= (y-\dfrac{1}{y})(y^2+1+\frac{1}{y^2}) ~~~~[\because~a^3-b^3=(a-b)(a^2+ab+b^2)]$

$\implies y^3-\dfrac 1 {y^3} = 6\times (38+1) ~~\left[\because ~ \left(y^2+\frac 1 {y^2} \right)= 38, ~\left(y-\dfrac{1}{y}\right)=6\right]$

$\implies y^3-\dfrac 1 {y^3} =234$

Hence, $y^3-\dfrac{1}{y^3}$= 234

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