Question

solution of under root x / Y + under root Y / x = 13 / 6 and xY = 36

Answer 1

first of all squaring both side and then using formula of (a+b) whole square and then solve
answer is x square + y square = 167

Answer 2

√X/√Y + √Y/√X = 13/6

GIVEN XY = 36

THEREFORE X = 36/Y

√X = 6/√Y

USING IN EQ.1

6/√Y/√Y + √Y/6/√Y = 13/6

6/Y + Y/6 = 13/6

36 + Y²/6Y = 13/6

36 +Y²/Y = 13

36 + Y² = 13Y

Y² - 13Y + 36 = 0

Y² - 4Y - 9Y +36 = 0

→ Y= 4                            AND Y= 9

NOW X = 36/Y

WHEN Y=4 X=36/4            AND WHEN Y = 9 X = 36/9

X = 9                                    X= 4