If-C-2x-x-70-prove-that-x-4-

Question Number 164429 by malwan last updated on 17/Jan/22

I f C (2 x, x) = 70

p r o v e t h a t x = 4

Answered by alephzero last updated on 17/Jan/22

C_{x}^{2 x} = 70

C_{x}^{2 x} = C_{4}^{8} = \frac{8!}{4! (8 - 4)!} = \frac{8!}{4! 4!} =

= \frac{2 \times 3 \times 4 \times 5 \times 6 \times 7 \times 8}{(2 \times 3 \times 4) (2 \times 3 \times 4)} =

= \frac{5 \times 2 \times 7 \times 2}{2} = 5 \times 2 \times 7 = 10 \times 7 =

= 70

\Rightarrow C_{x}^{2 x} = 70 \Leftrightarrow x = 4

Commented by malwan last updated on 17/Jan/22

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