solve the following quadratic equation by factorisation method : 6√3x^2+7x=√3 with full explaination!
Answers
Answer:
Given : (x - 2) / (x - 3) + (x - 4) / (x - 5) = 10/3
[( x - 2 ) ( x - 5) + (x - 4) (x - 3) ] /[ (x - 5) (x - 3) ] = 10/3
[ By taking LCM]
[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
3[2x² - 14x + 22] = 10 [x² - 8x + 15]
6x² - 42x + 66 = 10x² - 80x + 150
10x² - 6x² - 80x + 42 x + 150 - 66 = 0
4x² - 38x + 84 = 0
2(2x² - 19x + 42) = 0
2x² - 19x + 42 = 0
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
Hence, the roots of the quadratic equation (x - 2) / (x - 3) + (x - 4) / (x - 5) = 10/3 are 6 & 7/2
Answer:
Here is the answer
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