Question

$if \: {x}^{2} + {y}^{2} = 29 and \: xy = 2 \: find \: the \: value \: of \: (i)x + y \: (ii)x - y \: (iii) {x}^{4} + {y}^{4}$
​

Answer 1

x^2+y^2=29
xy=2

using identity (x+y)^2 or (a+b)^2

= x^2+y^2+2•x•y [now put in the required values]

= 29+2•2

=29+4

=33 Ans

hope it helps

Answer 2

Step by step-

(x+y)^2 = x^2 + y^2 + 2xy

Given: x^2+y^2=29 and xy=2

substitute these values

(x+y) ^2 = 29 +2(2)

(x+y)^2 = 33

Now square root both sides

x+y= +-√33

Now,

(x-y)^2 = x2 + y2 -2xy

Substitute the given values

(x-y) ^2= 29 - 2(2)

(x-y)^2 = 25

Square root both sides

x-y = +-5