Question 58

If $$1 + 9r^2 + 81r^4 = 256$$ and $$1 + 3r + 9r^2 = 32$$, then find the value of $$1 - 3r + 9r^2$$.

Solution

Given that $$1 + 3r + 9r^2 = 32$$

and let $$1 - 3r + 9r^2$$ be K

Multiply $$1 + 3r + 9r^2$$ and $$1 - 3r + 9r^2$$

we get the product as $$1 + 9r^2 + 81r^4$$ = 32K

but $$1 + 9r^2 + 81r^4$$= 256
substitute this value in the product

256 = 32k

K=8

Therefore, answer is option B

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