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Algebra and Applications Test 1

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Question : 21 of 40

Marks: +1, -0

If

(a + b) = 4

ab = \frac{7}{4}

, what is the value of

a^2 - b^2

?

12
-12
12, -12
0

Solution: 👈: Video Solution

(a + b) = 4

...(i)

and

ab = \frac{7}{4} \Rightarrow b = \frac{7}{4a}

......(ii)

Substituting this value in equation (i) we get:

a + \frac{7}{4a} = 4

4a^2 + 7 = 16a

4a^2 - 16a + 7 = 0

4a^2 - 2a - 14a + 7 = 0

2a(2a - 1) - 7(2a - 1) = 0

(2a - 1) (2a - 7) = 0

a = \frac{1}{2}, \frac{7}{2}

a = \frac{7}{2}, \text{So } b = \frac{1}{2}

Now,

a^2 - b^2 = \left(\frac{7}{2}\right)^2 - \left(\frac{1}{2}\right)^2 = 12

Now,

a = \frac{1}{2}\text{So } b = \frac{7}{2}

a^2 - b^2 = \left(\frac{1}{2}\right)^2 - \left(\frac{7}{2}\right)^2 = -12

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