Question

If `4x^2+1/(9x^2)=14 2/3, "find" (2x +1/(3x)).`

Answer 1

Convert the mixed fraction to improper form:

`14 2/3=14 + 2/3`

14 × 3 = 42 

42 + 2 = 44

`∴14 2/3 = 44/3`

Let us assume that,

A = `2x + 1/(3x)`​

Now square the A = `2x + 1/(3x)`​,

A² = `(2x + 1/(3x))^2`

= `4x^2 + 2xx2x xx1/(3x) + 1/(9x^2)`

= `4x^2 + 4/3 + 1/(9x^2)`

Also, we know that,

`4x^2 + 1/(9x^2)` 

A² = `44/3 + 4/3`

A² = `48/3`

A² = 16

∴ A = `sqrt16`

∴ A = 4

Hence, `2x+1/(3x) = 4`