Question

a+b+c=10,a square +b square +c square =38,a cube +b cube +c cube =160 ,then the value of abc is

Answer 1

The value of abc is 30.
a is 2,b is 3 and c is 5.

Answer 2

Answer:

The value of abc is 30.

Explanation:

It is given that,

$a+b+c = 10$

$a^{2} + b^{2} + c^{2} = 38$

$a^{3} + b^{3} + c^{3}= 160$

Now, by using formula -

$( a+b+c )^{2} = a^{2}+b^{2}+c^{2}+2(ab+bc+ca)$

By putting all the given values,we get,

$(10)^{2} = 38+2(ab+bc+ca)$

$100 = 38+2(ab+bc+ca)$

By subtracting 38 from 100 and then dividing it with 2, we get -

$ab+bc+ca = 100-\frac{38}{2} = \frac{62}{2} = 31$

∴ $ab+bc+ca = 31$

$a^{3}+b^{3}+c^{3}-3abc = (a+b+c)(a^{2}+b^{2}+c^{2} -ab-bc-ca)$

 

As we know that,

$a^{3}+b^{3}+c^{3} = 160$

By using formula -

$a^{3}+b^{3}+c^{3}-3abc = (a+b+c)(a^{2}+b^{2}+c^{2} -ab-bc-ca)$

By putting all the given values, we get -

$160-3abc = 10( 38 -31 )\\ 160-3abc = 70\\ abc = 160-70/3 \\ abc = 30$

So,the value of abc is 30.

A mathematical statement with two equal algebraic expressions is called an algebraic equation. When P and Q are polynomials, the general form of an algebraic equation is P = 0 or P = Q. Equations in algebra with only one variable are referred to as univariate equations, while equations with several variables are referred to as multivariate equations. The solution of an algebraic equation is always balanced. This implies that the left and right sides of the equation will be equal.

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