Question

If a=2and b=3 then find the value of the following
(a÷b+b÷a)³

Answer 1

Answer:

$(\frac{a}{b} +\frac{b}{a})^{3}$=  $\frac{2197}{216}$ if $a=2$ and $b=3$.

Step-by-step explanation:

Given : The expression is $(\frac{a}{b} +\frac{b}{a})^{3}$, $a$=$2$ and $b=3$

To find : The value of above equation.

Solution :

• The given expression is,  $(\frac{a}{b} +\frac{b}{a})^{3}$
• The values of $a$ and $b$ are given.

       $a=2$ and $b=3$

• Now, put these values in given equation,we get

     $(\frac{a}{b} +\frac{b}{a})^{3}$ = $(\frac{2}{3}+\frac{3}{2} )^{3}$

• Carrying out cross multiplication, we get

             = $(\frac{2*2+3*3}{2*3} )^{3}$

             = $(\frac{4+9}{6})^{3}$

             = $(\frac{13}{6})^{3}$

             = $\frac{2197}{216}$      (∵$13^{3} =2197, 6^{3}=216$)

• ∴  $(\frac{a}{b} +\frac{b}{a})^{3}$=  $\frac{2197}{216}$ if $a=2$ and $b=3$.

Answer 2

Given: $a=2, b=3$

We have to find the value of$(a\div b+b\div a)^{3}$.

For this, we will put the value of a and b in the given equation, and then we will add the equation.

And after that, we will find the cube of the value.

We are solving in the following way:

We have $a=2, b=3$

$=>(2\div 3+3\div2)^{3} \\\\=>(\frac{2}{3} +\frac{3}{2} )^{3} \\\\=>(\frac{2\times 2+3\times 3}{3\times 2} )^{3}$

$=>(\frac{4+9}{6} )^{3} \\\\=>(\frac{13}{6} )^{3}$

Solving the above equation further we get,

$=>\frac{2197}{216} \\\\=>10.171$

Hence, the value of $(a\div b+b\div a)^{3}$will be$10.171$.