An algebra problem by Viki Zeta

Algebra Level 2

( 4 + + 4 ) x 2 times ( x + + x ) x times 2 = ? \frac{(\underbrace{4 + \cdots + 4)}_{x^2\text{ times}}}{\underbrace{(x + \cdots+ x)}_\text{x times}} - 2 = \, ?

Find the value of the above expression given that k k is a non-zero real number and x x is a natural number.


The answer is 2.

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1 solution

Viki Zeta
Jul 2, 2016

4 + ... + 4 x 2 times x + ... + x x times 2 = 4 x 2 x 2 2 = 4 2 = 2 \frac{\underbrace{4 + \text{ ... } + 4}_{x^2\text{ times}}}{\underbrace{x + \text{ ... } + x}_\text{x times}} - 2 \\ = \frac{4x^2}{x^2} - 2 \\ = 4 - 2 \\ = 2

Here 4 + ... + 4 x 2 times \underbrace{4 + \text{ ... } + 4}_{x^2\text{ times}} is equal to 4 x 2 4x^2 as, 4 is added upto x 2 x^2 times. Like 4 + 4 + 4 = 3 4 4 + 4 + 4 = 3 * 4 , 4 + 4 + 4 + . . . + x 2 times 4 = 4 x 2 4+4+4+...+x^2 \text{ times } 4 = 4x^2 . Similarly for denominator.

You should specify that x 0 x \neq 0 to avoid undefined values.

Alex G - 4 years, 11 months ago

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CLARIFIED |x|>0

Viki Zeta - 4 years, 11 months ago

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