​If x² + y² – 4x + 8y + 20 = 0, then the value of x² + y² is:

Correct option is B

​Given:
Equation: $$x^2 + y^2 - 4x + 8y + 20 = 0$$​​

Formula Used:

$$(a+b)^2 = a^2+b^2+2ab$$​​​

Solution:
​$$x^2 + y^2 - 4x + 8y + 20 = 0$$ 

this can be written as 

​$$x^2 + y^2 - 2 \times 2\times x + 2\times 4 \times y + 16 + 4 = 0 \\ \ \\ x^2- 2 \times 2\times x +4 +y^2+2\times 4 \times y+16 = 0 \\ \ \\ (x-2)^2 + (y+4)^2 = 0$$​​

This can only be 0 when 

x = 2 and y = -4 

So, 

value of $$x^2+y^2 = 2^2 +(-4)^2 = 20$$​​

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