Math, asked by gauravrrajput, 10 months ago

If x2 + y2 = 4 and x - y = 3 then find the value of x3-y3.​

Answers

Answered by Anonymous
10

Answer:

\large\bold\red{\frac{9}{2}}

Step-by-step explanation:

Given,

 {x}^{2}  +  {y}^{2}  = 4

And,

x - y = 3

Now,

We have to find the value of,

 {x}^{3}  -  {y}^{3}

But,

We know that,

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

Also,

We know that,

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

Therefore,

Putting the values,

We get,

 =  >  {3}^{2}  = 4 - 2xy   \\  =  > 2xy = 4 - 9 \\  =  > xy =  -  \frac{5}{2}

Putting this value,

We get,

  =  > {x}^{3}  -  {y}^{3}  = 3(4  + ( -  \frac{5}{2} ) \\ \\   =  >  {x}^{3}  -  {y}^{3}  = 3(4 -  \frac{5}{2} ) \\ \\    =  >  {x}^{3}  -  {y}^{3}  = 3( \frac{8 - 5}{2} ) \\ \\   =  > {x}^{3}    -  {y}^{3} = 3 \times  \frac{3}{2}   \\  \\  =  >  \large \boxed{  \bold{{x}^{3}  -  {y}^{3}  =  \frac{9}{2} }}

Answered by RvChaudharY50
40

Given :-----

  • + = 4
  • (x - y) = 3

To Find :----

  • ( - )

Formula used :----

  • ( - ) = (x-y)(++xy)
  • (x - y)² = + - 2xy

Let, ( x - y) = 3 ---------------- Equation (1)

Squaring both sides of Equation (1) we get,

(x - y)² = 3²

→ x² + y² - 2xy = 9

Putting value of (x²+y² = 4) Now we get,

→ 4 - 2xy = 9

→ (-2xy) = 9-4

→ xy = (-5/2) ------------------------- Equation (2)

Now, we have to find ( - )

(x³ - y³) = (x-y)(x²+y²+xy)

Putting all our values in this formula we get,,

( {x}^{3}  -  {y}^{3} ) = 3(4 + ( \frac{ - 5}{2} )) \\  \\  \implies \: ( {x}^{3}  -  {y}^{3} ) = 3( \frac{8 - 5}{2} ) \\  \\\implies \:  ( {x}^{3}  -  {y}^{3} ) = 3( \frac{3}{2} ) \\  \\ \implies( {x}^{3}  -  {y}^{3} ) =  \frac{9}{2}

So Value of (x³ - y³) will be = \red{\bold{\frac{9}{2}}}

(Hope it Helps you)

______________________________

\large\bold\star\underline\mathcal{Extra\:Brainly\:Knowledge:-}

[1] ( a + b )² = a² + 2ab + b²

[2] ( a – b )² = a² – 2ab + b²

[3] ( a + b )³ = a³ + 3a² b + 3ab² + b³

[4] ( a – b )³ = a ³ – 3a² b + 3ab² – b³

[5] ( a + b )( a ² - ab + b² ) = a³ + b³

[6] ( a – b )( a ² + ab + b² ) = a³ – b³

\mathcal{BE\:\:BRAINLY}

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