Question

Evaluate:0.57*0.57*0.57+0.43*0.43*0.43/0.57*0.57-0.57*0.43+0.43*0.43

Answer 1

Step-by-step explanation:

Given :-

0.57*0.57*0.57+0.43*0.43*0.43/0.57*0.57-0.57*0.43+0.43*0.43

To find:-

Evaluate:0.57*0.57*0.57+0.43*0.43*0.43/0.57*0.57-0.57*0.43+0.43*0.43

Solution:-

Given numerical expression is

0.57×0.57×0.57+0.43×0.43*0.43/0.57×0.57-0.57 × 0.43+0.43×0.43

It can be written as

[(0.57)^3+(0.43)^3]/[(0.57)^2-(0.57)(0.43)+(0.43)^2]

It is in the form of (a^3+b^3)/(a^2-ab+b^2)

Where a = 0.57 and b = 0.43

We know that

a^3+b^3 = (a+b)(a^2-ab+b^2)

=>(a^3+b^3)/(a^2-ab+b^2)

= (a+b)(a^2-ab+b^2)/(a^2-ab+b^2)

= (a+b)

Now

[(0.57)^3+(0.43)^3]/[(0.57)^2-(0.57)(0.43)+(0.43)^2]

=> 0.57+0.43

=> 1.00

=> 1

Answer:-

The value of 0.57×0.57×0.57+0.43×0.43*0.43/0.57×0.57-0.57 × 0.43+0.43×0.43 is 1

Used formula:-

• a^3+b^3 = (a+b)(a^2-ab+b^2)

• (a^3+b^3)/(a^2-ab+b^2) = a+b