Question

Ifx-y=5 and xy=6find the value of x^3-y^3

Answer 1

$\large\underline{\sf{Solution-}}$

Given that,

$\red{\rm :\longmapsto\:x - y = 5}$

and

$\red{\rm :\longmapsto\:xy = 6}$

Now, Consider

$\green{\rm :\longmapsto\: {x}^{3} - {y}^{3}}$

$\green{\rm \: = \: {(x - y)}^{3} + 3xy(x - y)}$

On substituting the values, we get

$\green{\rm \: = \: {5}^{3} + 3 \times 5 \times 6}$

$\green{\rm \: = \: 125 + 90}$

$\green{\rm \: = \: 215}$

$\red{\bf\implies \:\boxed{ \tt{ \: {x}^{3} - {y}^{3} = 215 \: }}}$

More Identities to know :-

$\green{\boxed{ \tt{ \: {(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2} \: }}}$

$\green{\boxed{ \tt{ \: {(x - y)}^{2} = {x}^{2} - 2xy + {y}^{2} \: }}}$

$\blue{\boxed{ \tt{ \: {(x + y)}^{3} = {x}^{3} + {y}^{3} + 3xy(x + y) \: }}}$

$\blue{\boxed{ \tt{ \: {(x - y)}^{3} = {x}^{3} - {y}^{3} - 3xy(x - y) \: }}}$

$\purple{\boxed{ \tt{ \: {x}^{3} + {y}^{3} = {(x + y)}^{3} - 3xy(x + y) \: }}}$

$\purple{\boxed{ \tt{ \: {x}^{3} - {y}^{3} = {(x - y)}^{3} + 3xy(x - y) \: }}}$

$\purple{\boxed{ \tt{ \: {x}^{3} - {y}^{3} = (x - y)( {x}^{2} + xy + {y}^{2} ) \: }}}$

$\purple{\boxed{ \tt{ \: {x}^{3} + {y}^{3} = (x + y)( {x}^{2} - xy + {y}^{2} ) \: }}}$

$\purple{\boxed{ \tt{ \: {x}^{2} - {y}^{2} = (x + y)(x - y) \: }}}$

$\purple{\boxed{ \tt{ \: {x}^{4} - {y}^{4} = (x + y)(x - y)( {x}^{2} + {y}^{2})\: }}}$

Answer 2

$\huge \red{ \boxed{ \bf \blue{215}}}$

Step-by-step explanation:

GIVEN :-

$\bf \color{orange}{x - y = 5} \\ \\ \bf \color{skyblue}{xy = 6}$

TO FIND :-

$\bf \color{lime}{ {x}^{3} - {y}^{3} }$

SOLUTION :-

We know that,

$\color{maroon}{ \boxed{ \bf \color{yellow}{ {x}^{3} - {y}^{3} } = \color{red}{ {(x - y)}^{3} + 3xy(x - y)}}}$

By Substituting values we get,

$= \bf \color{green} {(5)}^{3} + 3(6)(5) \\ \\ = \bf \color{blue}125 + 90 \\ \\ = \large \underline{ \overline{\bf \color{purple}{215}}}$

Hence,

The value of x³ - y³ = 215.

Hope it helps.

#BeBrainly :-)