Question 15

If $$a^2 + b^2 = 4b + 6a - 13$$, then what is the value of $$a + b$$

Solution

$$a^2+b^2=4b+6a-13$$

or, $$a^2+b^2-4b-6a-13=0\ .$$

or, $$\left(a^2-2.3.a+3^2\right)+\left(b^2-2.2.b+2^2\right)=0\ .$$

or, $$\left(a-3\right)^2+\left(b-2\right)^2=0\ .$$

So, $$\left(a-3\right)=0\ and\ \left(b-2\right)=0\ .$$

or, $$\left(a=3\right)\ and\ \left(b=2\right)\ .$$

So, a+b=5 .

C is correct choice.

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