Question 20

If $$(a + b)^2 - 2(a + b) = 80$$ and $$ab = 16$$, then what is the value of $$3a - 19b$$?

Solution

$$(a+b)^2-2(a+b)=80$$

or, $$(a+b)^2-2(a+b)+1=80+1\ .$$

or, $$(a+b-1)^2=9^2\ .$$

or, $$(a+b-1)=9\ .$$

or, $$(a+b)=10\ ..............\left(1\right)$$

Now, $$(a-b)^2=\left(a+b\right)^2-4ab=100-4.16=36\ .$$

or, $$(a-b)=6\ .................\left(2\right)$$

By solving (1) & (2) we get :

a=8 and b=2 .

So, $$3a-19b=3\times8-19\times2=-14\ .$$

B is correct choice.

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