Question

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

Answer 1

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,

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

Answer 2

Given :-----

• x² + y² = 4
• (x - y) = 3

To Find :----

• (x³ - y³)

Formula used :----

• (x³ - y³) = (x-y)(x²+y²+xy)
• (x - y)² = x² + y² - 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)

(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

$\mathcal{BE\:\:BRAINLY}$