solve the following quadratic equation by factorisation x minus 2 upon x minus 3 plus x minus 4 upon x minus 5 is equals to 10 upon 3
Answers
Given : x minus 2 upon x minus 3 plus x minus 4 upon x minus 5 is equals to 10 upon 3
To find: Solve the following quadratic equation by factorization?
Solution:
- Now we have given the equation as:
x-2/x-3 + x-4/x-5 = 10/3
- Now solving it, we get:
[( x - 2 ) ( x - 5) + (x - 4) (x - 3) ] /[ (x - 5) (x - 3) ] = 10/3
[x² - 5x - 2x + 10 + x² - 3x - 4x + 12] / [x² - 3x - 5x + 15] = 10/3
[2x² - 7x + 10 - 7x + 12] / [x² - 8x + 15] = 10/3
[2x² - 14x + 22] / [x² - 8x + 15] = 10/3
- Now cross multiplying, we get:
3[2x² - 14x + 22] = 10 [x² - 8x + 15]
6x² - 42x + 66 = 10x² - 80x + 150
- Taking all the terms on one side, we get:
10x² - 6x² - 80x + 42 x + 150 - 66 = 0
4x² - 38x + 84 = 0
2(2x² - 19x + 42) = 0
2x² - 19x + 42 = 0
- Now splitting middle terms, we get:
2x² - 12x - 7x + 42 = 0
2x(x - 6) - 7 (x - 6) = 0
(x - 6) (2x - 7) = 0
x - 6 = 0 or 2x - 7 = 0
x = 6 or 2x = 7
x = 6 or x = 7/2
Answer:
So the value of x can be 6 or 7/2.
- above is the answer and it is correct
