If A and B are whole numbers such that $9 A^{2} = 12 A + 96$ and $B^{2} = 2 B + 3$ , find the value of $5 A + 7 B$ .

31

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37

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41

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43

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Solution

The correct option is B $41$
A,B are whole numbers
$9 A^{2} = 12 A + 96$ & $B^{2} = 2 B + 3$
$9 A^{2} - 12 A - 96 = 0$ & $B^{2} - 2 B - 3 = 0$
$3 A^{2} - 4 A - 32 = 0$
$3 A^{2} - 12 A + 8 A - 32 = 0$ & $B^{2} - 3 B + B - 3 = 0$
$(3 A + 8) (A - 4) = 0$ & $(B - 3) (B + 1) = 0$
$∴ A = 4, B = 3$ ( $∵ A, B$ are whole numbers $∵ (A \neq \frac{- 8}{3})$ & $(B \neq - 1$ )
$5 A + 7 B = 5 (4) + 7 (3)$
$= 41$

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If a, b, and c are nonzero real numbers such that ab = 2 (a + b), bc = 3( b + c) and ca = 4 (c + a) then the value of 5a + 7b + c is :

If `a' and `b' are whole numbers such that b > 1 and a $^{b}$ = 144, what is the value of (a - 2) $^{b + 2}$ ?

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