If x2 + y2 = 4 and x - y = 3 then find the value of x3-y3.
Answers
Answer:
Step-by-step explanation:
Given,
And,
Now,
We have to find the value of,
But,
We know that,
Also,
We know that,
Therefore,
Putting the values,
We get,
Putting this value,
We get,
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,,
So Value of (x³ - y³) will be =
(Hope it Helps you)
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[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