Question

If x – y = 9 and xy = 36, find (i) x + y and (ii) x2 – y

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Answer 1

Answer:

x-y=9

x-9=y

xy=36

x(x-9)=36

x^2 - 9x = 36

x^2 - 9x - 36 =0

x^2 - 12x + 3x - 36 = 0

x(x -12) + 3(x - 12) = 0

(x - 12)(x + 3) = 0

x - 12 = 0

x = 12

x + 3 = 0

x = -3

If x = 12

y = x - 9

y = 12 - 9

= 3

Now,

i) x + y

= 12 + 3

= 15

ii) x^2 - y^2

=(12 × 12) - (3 × 3)

=144 - 9

=135

If x = -3

y = x - 9

= -3 - 9

= -12

Similarly solve i) and ii)