if x-y=3 and xy= 10 then find x ^4 + y^4
Answers
Answered by
14
Hey mate!!
(x - y) = 3 , xy = 10
(xy)² = 10²
x²y² = 100
So,
(x - y) = 3
squaring both sides
=> (x - y)² = (3)²
=> x² + y² - 2 xy = 9
=> x² + y² - 2 × 10 = 9
=> x² + y² = 9 + 20
=> x² + y² = 29
Again,
squaring both sides
(x² + y²)² = (29)²
x⁴ + y⁴ + 2x²y² = 841
x⁴ + y⁴ + 2 × 100 = 841
x⁴ + y⁴ + 200 = 841
x⁴ + y⁴ = 841 - 200
x⁴ + y⁴ = 641
Thanks for the question!!
(x - y) = 3 , xy = 10
(xy)² = 10²
x²y² = 100
So,
(x - y) = 3
squaring both sides
=> (x - y)² = (3)²
=> x² + y² - 2 xy = 9
=> x² + y² - 2 × 10 = 9
=> x² + y² = 9 + 20
=> x² + y² = 29
Again,
squaring both sides
(x² + y²)² = (29)²
x⁴ + y⁴ + 2x²y² = 841
x⁴ + y⁴ + 2 × 100 = 841
x⁴ + y⁴ + 200 = 841
x⁴ + y⁴ = 841 - 200
x⁴ + y⁴ = 641
Thanks for the question!!
ps284147:
how can x^2 *y^2 = x^2+y^2
and answr is 641
Where
where i have done mistake ?
let me check once
in the second step 2* x^2*y^2
Now, is it ok
thanks didi
Welcome lee :))
Answered by
18
Hey mate!!✌✌
✴FIND THE VALUE✴
(x - y) = 3 , xy = 10
(xy)² = 10²
x²y² = 100
So, (x - y) = 3
squaring both sides
=> (x - y)² = (3)²
=> x² + y² - 2 xy = 9
=> x² + y² - 2 × 10 = 9
=> x² + y² = 9 + 20
=> x² + y² = 29
Again,
Squaring both sides
=> (x² + y²)² = (29)²
=> x⁴ + y⁴ + 2x²y² = 841
=> x⁴ + y⁴ + 2 × 100 = 841
=> x⁴ + y⁴ + 200 = 841
=> x⁴ + y⁴ = 841 - 200
=> x⁴ + y⁴ = 641
Hence the answer is 641.
Thanks for the question!!
☺☺☺
✴FIND THE VALUE✴
(x - y) = 3 , xy = 10
(xy)² = 10²
x²y² = 100
So, (x - y) = 3
squaring both sides
=> (x - y)² = (3)²
=> x² + y² - 2 xy = 9
=> x² + y² - 2 × 10 = 9
=> x² + y² = 9 + 20
=> x² + y² = 29
Again,
Squaring both sides
=> (x² + y²)² = (29)²
=> x⁴ + y⁴ + 2x²y² = 841
=> x⁴ + y⁴ + 2 × 100 = 841
=> x⁴ + y⁴ + 200 = 841
=> x⁴ + y⁴ = 841 - 200
=> x⁴ + y⁴ = 641
Hence the answer is 641.
Thanks for the question!!
☺☺☺
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