Q.b ifx4+x2y2+y4= 21 and x² + xy + y2 = 7, then the Value of (1/x2+1/y2)is
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Answer:
| If x4 + x2y2 + y4 = 21, and x2 + xy + y2 = 3, then what is the value of 4xy?
A. -8
B. 4
C. -4
D. 12
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Step-by-step explanation:
Given:
If x4 + x2y2 + y4 = 21 and x2 + xy + y2 = 7
Formula used:
x4 + x2y2 + y4 = (x2 – xy + y2) (x2 + xy + y2)
Calculation:
x4 + x2y2 + y4 = 21 and
x2 + xy + y2 = 7 --- (1)
x4 + x2y2 + y4 = (x2 – xy + y2) (x2 + xy + y2)
⇒ 21 = (x2 - xy + y2) × 7
⇒ (x2 - xy + y2) = 21/7
⇒ (x2 - xy + y2) = 3 --- (2)
equation (1) from equation (2)
2xy = 4
⇒ xy = 2
⇒ (xy)2 = 4
From equation (1)
x2 + y2 = 7 – 2
⇒ x2 + y2 = 5
Now,
(1/x2 + 1/y2)
⇒ (x2 + y2)/(xy)2
⇒ 5/4
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