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WAEC Mathematics 2019 Paper

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Question : 22

Total: 50

If 2

{}^a

\sqrt{64}

\; \frac{b}{a}

= 3, evaluate a

{}^2 + b^{2}

250
160
90
48

Solution:

Concept:

Express the equation in powers of 2, then use the ratio to find

b

.

Explanation:

Given:

2^a = \sqrt{64}

Since

\sqrt{64} = 8

, we get

2^a = 8

.

Write

8

as

2^3

:

2^a = 2^3

.

So,

a = 3

.

It is given that

\frac{b}{a} = 3

.

Substitute

a = 3

:

\frac{b}{3} = 3

.

Thus,

b = 3 \times 3 = 9

.

Now evaluate

a^2 + b^2

:

3^2 + 9^2 = 9 + 81 = 90

.

Answer:

a^2 + b^2 = 90

, which is option C.

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