Ques 1) If x+y = 12 and xy=32, find the value of
х²+y²
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We are given :
☞ x + y = 12 . . . . . . (1)
☞ xy = 32 . . . . . . . (2)
Let's square on both sides for (1) using (2) :
☞ (x + y)² = x² + y² + 2xy = (12)²
☞ x² + y² + 2 (32) = 144
☞ x² + y² + 64 = 144
☞ x² + y² = 144 – 64
☞ x² + y² = 80
Know more :
☞ (a – b)² = a² + b² – 2ab
☞ (a + b) (a – b) = a² - b²
☞ (x + a) (x + b) = x² + (a + b)x + ab
☞ (a + b)³ = a³ + b³ + 3 ab (a + b)
☞ (a – b)³ = a³ – b³ – 3 ab (a – b)
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Therefore, the value of x² + y² is 80 when x + y = 12 and xy = 32.
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