If x^2 + y^2 - 4x - 4y + 8 = 0 then the value of x - y is:

Algebra and Applications Test 1

Question : 5 of 40

Marks: +1, -0

x^2 + y^2 - 4x - 4y + 8 = 0

then the value of

x - y

is:

Solution:

x ^2 + y^2 - 4x - 4y + 8 = 0

(x^ 2 - 4x + 4) + (y ^2 - 4y + 4) = 0

(x ^2 - 2 × 2 × x + 2^2 )

+ (y ^2 - 2 × 2 × y + (2)^2 ) = 0

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

x - 2 = y - 2

x = y

x - y = 0

or, Alternatively you can solve.

x^{2}+y^{2}-4 x-4 y+8=0

x^{2}+4-4 x+y^{2}+4-4 y=0

(x-2)^{2}+(y-2)^{2}=0

x-2=0, y-2=0

x=2, y=2

∴ x-y=2-2=0

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