#Confused101

Algebra Level 4

I f 2 x + 2 − x = 3 , W h a t i s t h e v a l u e o f 8 x + 8 − x ? C r e d i t s t o E n g r . M a l i n g If\\ { 2 }^{ x }+{ 2 }^{ -x }=3,\\ What\quad is\quad the\quad value\quad of\quad {8 }^{ x }+{ 8 }^{ -x }?\\ \\ \\ Credits\quad to\quad Engr.\quad Maling


The answer is 18.

Lance Joseph Esquejo by Lance Joseph Esquejo , 25, Philippines

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2 solutions

If a + b − c = 0 a+b-c = 0 ,then

a 3 + b 3 − c 3 = − 3 a b c a^{3}+b^{3}-c^{3} = -3abc - - - - - - - - - - - - - - - - I I

2 x + 2 − x − 3 = 0 2^{x}+2^{-x}-3 = 0

Comparing it with I I ,

We get the desired result as 18 \boxed{18}

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Ronald Overwater
Jan 5, 2015

3 3 = ( 2 x + 2 − x ) 3 = 2 3 x + 3 × 2 x + 3 × 2 − x + 2 − 3 x 3^3 = (2^x+2^{-x})^3=2^{3x}+3 \times 2^x + 3 \times 2^{-x} +2^{-3x}

27 = 8 x + 8 − x + 3 × ( 2 x + 2 − x ) = 8 x + 8 − x + 3 × 3 27 = 8^x + 8^{-x} + 3 \times (2^x + 2^{-x})=8^x + 8^{-x} + 3 \times 3

8 x + 8 − x = 27 − 9 = 18 8^x + 8^{-x} = 27 - 9 = \fbox{18}

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