Question

(361)power 3+ (139)power 3/361*361-361*139+139*139

Answer 1

Given :

$\frac{ {361}^{3} + {139}^{3} }{ {361}^{2} - (361 \times 139) + {139}^{2} }$

(equation 1)

To find :

Solve the above equation.

Solution :

This is a simple algebraic equation, in which we have to firstly observe the given equation,

so that we can find the required formula to use to solve the equation.

In this case, it looks like a 3 degree polynomial, so

According to basic algebraic formula :

${x}^{3} + {y}^{3} = (x + y)( {x}^{2} - xy + {y}^{2} )$

(equation 2)

to look similar as equation 1,

on dividing equation 2's LHS and RHS with

x² - xy + y²

we get,

$\\ \bf \: \frac{( {x}^{3} + {y}^{3} ) }{ ({x}^{2} - xy + {y}^{2} ) } = (x + y)$

(equation 3)

On observing equation 1 and equation 3,

we get that

x = 361

and

y = 139

On putting these values in equation 3,

we get,

$\\ \bf \: \frac{( {361}^{3} + {139}^{3} ) }{ ({361}^{2} - (361 \times 139)+ {139}^{2} ) } = (x + y)$

so

solution of above equation :

= x + y

= 361 + 139

= 500

So,

The solution of above equation = 500.