Question

The product of two numbers is 16x4-1. If one
4.
number is 2x – 1, find the other.​

Answer 1

Here , we have the information given -

The product of two numbers is 16x⁴ - 1 .

Factorising 16x⁴ - 1

=> 16 x⁴ - 1

=> ( 4 x² ) ² - 1

=> ( 4x² + 1)( 4x² - 1 )

=> ( 4x² + 1 )( ( 2x )² - 1 )

=> ( 4x² + 1 )( 2x + 1 )( 2x - 1 )

Now , one if the numbers is 2x - 1

=> Other number

=> ( 4x² + 1 )( 2x + 1 )

=> 8x³ + 4x² + 2x + 1 .

This is the required answer .

___________________

Answer 2

$\huge\sf\pink{Answer}$

☞ $\sf 8x^2 + 4x^2 + 2x + 1$

$\rule{110}1$

$\huge\sf\blue{Given}$

✭ The product of 2 Number is 16x⁴ - 1

$\rule{110}1$

$\huge\sf\gray{To \:Find}$

◈ The other Number?

$\rule{110}1$

$\huge\sf\purple{Steps}$

First let's factorise

»» $\sf 16 x^4 - 1$

»» $\sf( 4x^2)^2 - 1$

»» $\sf (4x^2+1)( 4x^2-1)$

»» $\sf (4x^2+1)( ( 2x )^2-1)$

»» ($\sf 4x^2 + 1 )( 2x + 1 )( 2x-1)$

$\sf\therefore$ One Number is $\sf\red{(2x-1)}$

➢ $\sf Other \ number$

➢ $\sf (4x^2+1)(2x +1)$

➢ $\sf \orange{8x^2+4x^2+2x+1}$

$\rule{170}3$