Solve the following quadratic equation; 3(7x+1/5x-3) -4 (5x-3/7x+1)= 11
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3(7x+1/5x-3) - 4 (5x-3/7x+1)= 11
On Putting 7x+1/5x-3 = y,
3y - 4/y = 11
(3y × y -4 ) / y = 11
3y² - 4 = 11y
3y² - 11 y - 4 = 0
3y² -12y + y - 4 = 0
3y ( y - 4) +1(y - 4)= 0
(3y +1) (y - 4)= 0
(3y +1) = 0 or (y - 4)= 0
y = -⅓ or y = 4
Case 1. y = -⅓
7x+1/5x-3 = - ⅓
3(7x+1) = -1(5x-3)
21x +3 = -5x +3
21x +5x = 3 -3
26x = 0
x = 0/26
x = 0
Case 2. y = 4
7x+1/5x-3 = 4
7x+1 = 4(5x-3 )
7x +1 = 20x -12
7x - 20x = -12-1
-13x = -13
x = 13/13
x = 1
Hence, the value of x= 0 or x = 1.
HOPE THIS WILL HELP YOU...
3(7x+1/5x-3) - 4 (5x-3/7x+1)= 11
On Putting 7x+1/5x-3 = y,
3y - 4/y = 11
(3y × y -4 ) / y = 11
3y² - 4 = 11y
3y² - 11 y - 4 = 0
3y² -12y + y - 4 = 0
3y ( y - 4) +1(y - 4)= 0
(3y +1) (y - 4)= 0
(3y +1) = 0 or (y - 4)= 0
y = -⅓ or y = 4
Case 1. y = -⅓
7x+1/5x-3 = - ⅓
3(7x+1) = -1(5x-3)
21x +3 = -5x +3
21x +5x = 3 -3
26x = 0
x = 0/26
x = 0
Case 2. y = 4
7x+1/5x-3 = 4
7x+1 = 4(5x-3 )
7x +1 = 20x -12
7x - 20x = -12-1
-13x = -13
x = 13/13
x = 1
Hence, the value of x= 0 or x = 1.
HOPE THIS WILL HELP YOU...
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