Question

find the value of 27x3-1/27x3 if x-1/9x=1

Answer 1

Concept

In these types of questions, we have to make the given  expression into finding expression by the use of multiplication, division, addition and subtraction etc. tools.

Given

We have given an expression $x-\frac{1}{9x} =1$ .

Find

We are asked to determine the value of $27x^3-\frac{1}{27x^3}$ .

Solution

We will start from the given expression and will end it in the finding expression.

Multiplying by 3 in the given expression, we get

$3x-\frac{1}{3x} =3$    ....(1)

Doing cubic on both of the sides, we get

$(3x-\frac{1}{3x})^3 =3^3$      ......(2)

Applying formula $(a-b)^3=a^3-b^3-3ab(a-b)$  in equation (2) by putting,$a=3x,b=\frac{1}{3x}$ ,  we get

$(3x)^3-(\frac{1}{3x} )^3-3(3x)(\frac{1}{3x})(3x-\frac{1}{3x}) =9\\\\27x^3-\frac{1}{27x^3} -3(3x-\frac{1}{3x}) =9$

Putting the value of equation (1) in above sentence, we get

$27x^3-\frac{1}{27x^3} -3(3) =9\\\\27x^3-\frac{1}{27x^3} -9 =9\\\\27x^3-\frac{1}{27x^3} =18$

Therefore, the value of the given expression $27x^3-\frac{1}{27x^3}$  is 18 .

#SPJ2