Math, asked by gmona3831, 16 days ago

Find the root of equation
1/2x-3 +1/x-5=5​

Answers

Answered by NewtonofINDIA
0

1/2x-3 + 1/x-5 = 5

x-5+2x-3 = 5(x-5)(2x-3)

3x-8 = 10x²-65x+150

10x²-68x+158 = 0

solve the quadratic

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Answered by krishpmlak
0

Answer:

Step-by-step explanation:

Given that,

(1 / 2x - 3 ) + ( 1 / x - 5 ) = 5

⇒ (x - 5) + (2x - 3) / ( 2x -3) ( x - 5 ) = 5

⇒ ( x - 5 + 2x - 3 ) / ( 2x -3) ( x - 5 ) = 5

⇒ (3x - 8 ) / (2x -3) (x - 5) = 5

⇒ 3x - 8 = 5 (2x - 3 ) ( x - 5 )

⇒ 3x - 8 = 5 ( 2x² - 10x - 3x + 15 ) (∵ - × + = - ; - × - = + )

⇒ 3x - 8 = 5 ( 2x² - 13x + 15 )

⇒ 3x - 8 = 10x² - 65x + 75

⇒ 10x² - 65x + 75 - 3x + 8 = 0 (∵transposing )

⇒ 10x² - 68x + 83 = 0

Comparing the given equation with ax²+ bx + c = 0,

We have a = 10 , b = - 68 and c = 83

∴ x = - b ± √ b² - 4ac /2a

= - ( - 68 ) ± √( - 68 )² - 4 ( 10 ) ( 83 ) / 2 ( 10 )

= 68 ± √ 4624 - 3320 / 20

= 68 ± √ 1304 / 20

∴ The roots of the equation are 68 + √1304 / 20 and 68 - √1304 / 20

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