Algebra and Applications Test 1

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Question : 21 of 40

Marks: +1, -0

If

(a + b) = 4

, and

ab = 7/4

, what is the value of

a^2 - b^2

?

12
-12
12, -12
0

Solution:

(a + b) = 4

...(i)
and

ab = 7/4⇒b=7/{4a}

......(ii)
Substituting this value in equation (i) we get:

a+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=1/2,7/2

a=7/2,\So b=1/2

Now,

a^2-b^2=(7/2)^2-(1/2)^2=12

Now,

a=1/2\So b=7/2

a^2-b^2=(1/2)^2-(7/2)^2=-12

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