If $$a+b=-8$$ and $$a=20/b$$ what is the value of $$a^2+b^2$$?

A. 24
B. 32
C. 34
D. 40
E. 104

The OA is A.

Please, can any expert assist me with this PS question? I don't have it clear and I appreciate if any explain it for me. Thanks.

Hi AAPL,
Let's take a look at your question.

$$a+b=-8$$
$$a=\frac{20}{b}$$
$$a^2+b^2=?$$

Starting from,
$$a+b=-8$$
Squaring both sides,
$$\left(a+b\right)^2=\left(-8\right)^2$$
Evaluating,
$$a^2+b^2+2ab=64...(i)$$

We know that,
$$a=\frac{20}{b}$$
Plugging value of a in (i),
$$a^2+b^2+2\left(\frac{20}{b}\right)b=64$$
$$a^2+b^2+2\left(20\right)=64$$
$$a^2+b^2+40=64$$
$$a^2+b^2=64-40$$
$$a^2+b^2=24$$

Therefore, Option A is correct.

Hope it helps.
I am available if you'd like any follow up.

AAPL wrote:If $$a+b=−8$$ and $$a=20/b$$ what is the value of $$a^2+b^2$$?

A. 24
B. 32
C. 34
D. 40
E. 104

We can square the first equation and we have:

a^2 + b^2 + 2ab = 64

Simplifying the second equation, we have:

ab = 20

Thus:

a^2 + b^2 + 40 = 64

a^2 + b^2 = 24

Answer: A