Math, asked by kkraokotana, 10 months ago

a root of the equation (x-2)(x-3)/=155*78/(77)²​

Answers

Answered by amitnrw
14

Given : (x - 2) (x - 3)  =   155 * 78  /  ( 77²)  

To find :  Roots

Solution:

(x - 2) (x - 3)  =   155 * 78  /  ( 77²)

155 * 78  /  ( 77²)  

= (2 * 77 + 1)  * (77 + 1) / 77²  

= (2 * 77²  + 2 * 77 +  77  + 1 )/77²

= (2 * 77²  +  3*77 + 1 )/77²

= 2    +3/77  +  1/77²

Let say  y   =   1/77

=  2 +  3y  +  y ²

=  2 +  2y + y + y²

= 2(1 + y) + y(1 + y)

= (2 + y) (1 + y)

=  (y + 2 )(y + 1)

Put y  = z  - 4

= ( z -4 +2) (z - 4 + 1)

= (z -2)(z - 3)

Compare with

(x - 2)(x - 3)

Hence x  = z

y = x - 4

=> x = y + 4

y =  1/77

=> x = 1/77 + 4

=> x = 309/77

x = 309 /77

309 /77   is the one root of the equation

Put y  = z  + 1  in (y + 2 )(y + 1)

= (z + 3)(z + 2)

= (-z - 3)(-z - 2)

comparing with (x - 2)(x - 3)

=> x = - z  => z = -x

=> y = -x  + 1

=> x = 1 - y

=> x = 1 -  1/77

=> x = 76/77

This is 2nd root

76/77  & 309/77 are the roots

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