find roots of 21x²-2x+1/21=0 by Factorisation method
Answers
Answer:
Required root of the given equation is 1 / 21.
Step-by-step explanation:
Given equation : 21x^2 - 2x + 1 / 21 = 0.
= > ( 21x^2 × 21 ) - ( 2x × 21 ) + 1 = 0 × 21
= > 441x^2 - 42x + 1 = 0
Using Factorisation :
Splitting the middle term( term having x ) so that the product of parts is equal to the product of coefficient of x^2 and the remaining term.
So here product of parts should be 441 x 1 = 441.
Required parts should be 21 and 21,since their product is 441.
= > 441x^2 - ( 21 + 21 )x + 1 = 0
= > 441x^2 - 21x - 21x + 1 = 0
= > 21x( 21x - 1 ) - ( 21x - 1 ) = 0
= > ( 21x - 1 )( 21x - 1 ) = 0
= > ( 21x - 1 )^2 = 0
= > x = 1 / 21
Or,
= > ( 21x^2 × 21 ) - ( 2x × 21 ) + 1 = 0 × 21
= > 441x^2 - 42x + 1 = 0
= > ( 21x )^2 - 2( 21x ) + 1 = 0
= > ( 21x - 1 )^2 = 0 { Using a^2 + b^2 - 2ab = ( a - b )^2 }
= > x = 1 / 21
Hence the required root of the given equation is 1 / 21.
Answer:
441x²- 42x + 1 = 0
(21x)² - (21x) +1 = 0
(21x-1)²= 0 {using a² + b²-2ab = (a-b)²}
x = 1/21.
hope it helps you..!!