Question

Prove that 0.75×0.75×0.75+0.25×0.25×0.25 divided by 0.75×0.75 -0.75×0.25+0.25×0.25 =1

Answer 1

Use BODMAS rule and solve the LHS which will be equal to RHS. That's how you can prove it.

Answer 2

Answer and Explanation:

To prove : Expression $0.75\times 0.75\times 0.75+0.25\times 0.25\times 0.25$ divided by $0.75\times 0.75 -0.75\times 0.25+0.25\times 0.25$ = 1

Solution :

We have to show,

$\frac{0.75\times 0.75\times 0.75+0.25\times 0.25\times 0.25}{0.75\times 0.75 -0.75\times 0.25+0.25\times 0.25}=1$

Let us assume x=0.75 and y=0.25

Then, $\frac{x\times x\times x+y\times y\times y}{x\times x -x\times y+y\times y}=1$

$\frac{x^3+y^3y}{x^2 -xy+y^2}=1$

Now, Taking LHS,

$LHS=\frac{x^3+y^3y}{x^2 -xy+y^2}$

We know that, $x^3+y^3=(x+y)(x^2+y^2-xy)$

$LHS=\frac{(x+y)(x^2+y^2-xy)}{x^2 -xy+y^2}$

Cancel the like terms,

$LHS=x+y$

Substitute the values of x and y,

$LHS=0.75+0.25$

$LHS=1$

$LHS=RHS$

Hence proved.