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.
If a+b=−8, and a=20/b, what is the value of a^2+b^2?
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Given: a+b=−8 and a=20/bAAPL 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
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.
Take a=20/b and multiply both sides by b to get: ab = 20
Take a + b = −8 and SQUARE both sides to get (a+b)² = (−8)²
Expand and simplify left side to get: a² + 2ab + b² = 64
Now replace ab with 20 to get: a² + 2(20)+ b² = 64
Simplify: a² + 40 + b² = 64
Subtract 40 from both sides to get: a² + b² = 24
Answer: A
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Brent
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Hi AAPL,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.
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.
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We can square the first equation and we have: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
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
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