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Find the number of values of x(x is real) for which 64 1/x +48 1/x =80 1/x

Find the number of values of x(x is real) for which 641/x+481/x=801/x

Grade:Upto college level

1 Answers

askIITiansexpert nagesh
16 Points
12 years ago

 

Given, 641/x+481/x = 801/x

Let y= 1/x

Then the equation is 64y+48y = 80y

Divide by 16y on both sides, we get

3y + 4y = 5y

It is of form

sinyz + cosyz =1,    where sinz=3/5,cosz=4/5

now above equality is true iff y=2, Since sinz≠0,±1

→ x=1/2

hence number of solutions is 1.

 

 

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