Question

If 99 × 21 - $\sqrt[3]{x}$ = 1968. Then find the value of x. \begin{align} & \text{a) 1367631} \\ & \text{b) 1366731} \\ & \text{c) 1367} \\ & \text{d) 111} \\ \end{align}

Hint: Now we have one equation in one variable. Hence we can easily find x by just shifting the terms. But here we have a cube root of x hence once we find the value of the cube root is x we will just take the cube on both the sides and hence find x.

Now the given equation is 99 × 21 - $\sqrt[3]{x}$ = 1968 ……………(1)
Here using distributive property we get 99 × 21 = (100-1) × 21 = 100 × 21 – 1 × 21
Hence 99 × 21 = 2100 – 21 = 2079
Substituting this in equation (1) we get 2079 - $\sqrt[3]{x}$=1968
Now taking2079 to the right hand side we get
-$\sqrt[3]{x}$=1968-2079
-$\sqrt[3]{x}$=-111
Now multiplying the above equation by -1.
$\sqrt[3]{x}$=111
Now taking cube on both the sides we get
${{\left( \sqrt[3]{x} \right)}^{3}}={{111}^{3}}$
Now we know that cube of cube root of x equals to x, using this we get.
\begin{align} & x=111\times 111\times 111 \\ & x=12321\times 111 \\ & x=1367631 \\ \end{align}

Hence we get the value of x as 1367631

Note: At the first step we might feel like directly taking cube on both the sides though the equation can also be solved taking cube in the first step it will be a little tedious to do so hence it is better to first take everything except cube root on RHS and then solve.