Question

If a2+b2=80 and ab = 32, then calculate the value of a-b/a+b.

A) 0.337 B) 0.339 C) 0.333 D) 0.335

Answer 1

Answer:

C)0.333

Step-by-step explanation:

a²+b²=80

ab=32

(a+b)²=a²+b²+2ab = 80+62=142

a+b=√144 = 12

(a-b)²=a²+b²-2ab=80-64=16

(a-b)=4

a-b / a+b = 4/12 = 1/3 = 0.333

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Answer 2

The answer is option c) 0.333

Step-by-step explanation:

Given: $a^2+b^2=80$ and $ab = 32$

To find: $\frac{a-b}{a+b}$

Solution:

• Using the identity $(a+b)^2 = a^2 + b^2 +2ab$

Now, substituting the values of  $a^2+b^2=80$ and $ab = 32$ in the identity, we obtain

$(a+b)^2 = 80 +2\times 32 = 80 +64 = 144$

$(a+b) =\sqrt{144} =12$

• Now, Using the identity $(a-b)^2 = a^2 + b^2 -2ab$

Again, substituting the values of  $a^2+b^2=80$ and $ab = 32$ in the identity, we obtain

$(a-b)^2 = 80 -2\times 32 = 80 -64 = 16$

$(a+b) =\sqrt{16} =4$

• So, $\frac{a-b}{a+b} = \frac{4}{12}= \frac{1}{3} = 0.333$

Hence, the answer is option c) 0.333