If the summation of roots of two integers is √(11+8√2). What is the summation of the squares of these two integers?
Solution
Correct Answer: Option C
Let,
The two integers are x and y.
ATQ,
√x + √y = √(11 + 8√2)
⇒ (√x + √y)2 = {√(11 + 8√2)}2
⇒ x + 2√x . √y + y = 11 + 8√2
⇒ x + y + 2√(xy) = 11 + 8√2
So, x + y = 11
And,
2√(xy) = 8√2
⇒ √(xy) = 4√2
⇒ xy = 32
Now,
(x + y)2 = 112
⇒ x2 + y2 + 2xy = 121
⇒ x2 + y2 = 121 - 2 . 32
⇒ x2 + y2 = 57
The two integers are x and y.
ATQ,
√x + √y = √(11 + 8√2)
⇒ (√x + √y)2 = {√(11 + 8√2)}2
⇒ x + 2√x . √y + y = 11 + 8√2
⇒ x + y + 2√(xy) = 11 + 8√2
So, x + y = 11
And,
2√(xy) = 8√2
⇒ √(xy) = 4√2
⇒ xy = 32
Now,
(x + y)2 = 112
⇒ x2 + y2 + 2xy = 121
⇒ x2 + y2 = 121 - 2 . 32
⇒ x2 + y2 = 57
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