Question

cube of 361-cube of 139 divided by square of 361-361*139+square of 139

Answer 1

$\dfrac{361^3+139^3}{361^2-361\times 139+139^{2}}=500$

Step-by-step explanation:

We have,

$\dfrac{361^3+139^3}{361^2-361\times 139+139^{2}}$

To find, $\dfrac{361^3+139^3}{361^2-361\times 139+139^{2}}=?$

∴ $\dfrac{361^3+139^3}{361^2-361\times 139+139^{2}}$

Using algebraic identity,

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

∴ $\dfrac{(361+139)(361^2-361\times 139+139^{2})}{361^2-361\times 139+139^{2}}$

= 361 + 139

= 500

Hence, $\dfrac{361^3+139^3}{361^2-361\times 139+139^{2}}=500$.

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Answer 2

Step-by-step explanation:

361

2

−361×139+139

2

361

3

+139

3

To find, \dfrac{361^3+139^3}{361^2-361\times 139+139^{2}}=?

361

2

−361×139+139

2

361

3

+139

3

=?

∴ \dfrac{361^3+139^3}{361^2-361\times 139+139^{2}}

361

2

−361×139+139

2

361

3

+139

3

Using algebraic identity,

a^{3}+b^{3}=(a+b)(a^{2}+ab+b^{2})a

3

+b

3

=(a+b)(a

2

+ab+b

2

)

∴ \dfrac{(361+139)(361^2-361\times 139+139^{2})}{361^2-361\times 139+139^{2}}

361

2

−361×139+139

2

(361+139)(361

2

−361×139+139

2

)

= 361 + 139

= 500

Hence, \dfrac{361^3+139^3}{361^2-361\times 139+139^{2}}=500

361

2

−361×139+139

2

361

3

+139

3

=500 .

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