This Math Question Looks Easy… Until You Try It #maths #math

#brainexercise #matholympics
This Math Question Looks Easy… Until You Try It #maths #math

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[NadiehFan]

This question not only looks easy, it _is_ easy. We are given that

x + 1/(16x) = 3

and asked to evaluate

16x³ + 1/(256x³)

Observe that

x + 1/(16x) = (1/4)·(4x + 1/(4x))

so

4x + 1/(4x) = 12

and

16x³ + 1/(256x³) = (1/4)·(64x³ + 1/(64x³)) = (1/4)·((4x)³ + 1/(4x)³)

Now, let

4x = a, 1/(4x) = b

then we have

a + b = 4x + 1/(4x) = 12
a·b = 4x·(1/4x) = 1

and therefore

(4x)³ + 1/(4x)³ = a³ + b³
= (a + b)³ − 3ab(a + b)
= 12³ − 3·1·12
= 12·(12² − 3)

which gives

16x³ + 1/(256x³) = (1/4)·((4x)³ + 1/(4x)³) = 3·(12² − 3) = 3·141 = 423