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