Step-by-step explanation:
We have:
x - y = 43 , xy = 15
To find, the value of x^2+y^2x
2
+y
2
= ?
∴ x - y = 43
Squaring both sides, we get
(x - y)^2(x−y)
2
= 43^243
2
⇒ x^2+y^2x
2
+y
2
- 2xy = 1849
Using the algebraic identity,
(a - b)^2(a−b)
2
= a^2+b^2a
2
+b
2
- 2ab
⇒ x^2+y^2x
2
+y
2
= 1849 + 2xy
Put xy = 15, we get
x^2+y^2x
2
+y
2
= 1849 + 2(15)
⇒ x^2+y^2x
2
+y
2
= 1849 + 30
⇒ x^2+y^2x
2
+y
2
= 1879
∴ x^2+y^2x
2
+y
2
= 1879
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