Question

1 .If x + y = 12 and xy = 14, find the value of (x² + y²).
2.If x - y = 7 and xy = 9, find the value of (x2+y?).
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Answer 1

★${\boxed{\large{\bold{Solution\:1\::-}}}}$

• x + y = 12
• xy = 14

Now find the value of x² + y² .

→ x² + y²

• Use identity : a²+b² = (a+b)² - 2ab

→ (x+y)² - 2xy

• Put values : x+y = 12 and xy = 14

→(12)² - 2×14

→ 144 - 28

→ 116 [ Answer ]

__________________

★${\boxed{\large{\bold{Solution\:2\::-}}}}$

• x-y = 7
• xy = 9

Now find the value of x²+y² .

→ x² + y²

• Use identity : a²+b² = (a-b)² + 2ab

→ (x+y)² - 2xy

• Put values : x-y = 7 and xy = 9

→(7)² + 2×9

→ 49 + 18

→ 67 [ Answer ]

__________________

Some identities :-

★ (a+b)² = a² + 2ab + b²

★ (a-b)² = a² - 2ab + b²

★ a² - b² = (a+b) (a-b)

★ a²+b² = (a-b)² + 2ab

★ a²+b² = (a+b)² - 2ab