if x=y is root 5 and x-y is root 3 then what is x² + y²
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If x+y = 3 √8 , x-y = √2 , then the value of 8xy (x²+y²) is?
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7 Answers
Girija Warrier, former currently a teacher
Answered December 3, 2017 · Author has 3.2K answers and 4.6M answer views
(x + y)² = x² + y² + 2xy = (3√8)² = 72 ……..(1)
(x - y) ² = x² + y² -2xy = (√2)² = 2 ………..(2)
Eq(1) - eq(2) = 4xy = 70
=> 2xy = 35
=> 8xy = 140 …………(3)
(x + y)² = x² + y² +2xy
=> x² + y² = (x+y)² - 2xy
=> x² + y² = 72 - 35 = 37 ………….(4)
Now, by multiplying (3) & (4)
We get, 8xy ( x² + y² )
= 140 x 37
= 5180