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Solve the following equations using transposition method and check the solution the question is 3 x -2/4+x=2/3-2x+3/3?
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Solve the following equations using transposition method and check the...
Transposition method to solve the equation:
1. Given equation: 3x - 2/(4+x) = 2/3 - 2x + 3/3
2. First, simplify the equation:
3x - 2/(4+x) = 2/3 - 2x + 1
3x - 2/(4+x) = 2/3 - 2x + 1 (as 3/3 = 1)
3x - 2/(4+x) = 5/3 - 2x
3. Get rid of the fractions:
Multiply each term by (4+x) to get rid of the fraction:
3x(4+x) - 2 = (5/3 - 2x)(4+x)
12x + 3x^2 - 2 = 20 + 5x - 8x^2
4. Simplify the equation:
3x^2 + 12x - 2 = 20 - 3x^2
6x^2 + 12x - 22 = 0
5. Solve the quadratic equation:
Use the quadratic formula to find the roots of the equation:
x = (-b ± √(b^2 - 4ac)) / 2a
x = (-12 ± √(12^2 - 4*6*(-22))) / 2*6
x = (-12 ± √(144 + 528)) / 12
x = (-12 ± √672) / 12
x = (-12 ± 26√3) / 12
6. Check the solution:
Substitute the value of x back into the original equation to check if it satisfies the equation.
Therefore, the solutions to the equation 3x - 2/(4+x) = 2/3 - 2x + 3/3 are x = (-12 + 26√3) / 12 and x = (-12 - 26√3) / 12.
1. Given equation: 3x - 2/(4+x) = 2/3 - 2x + 3/3
2. First, simplify the equation:
3x - 2/(4+x) = 2/3 - 2x + 1
3x - 2/(4+x) = 2/3 - 2x + 1 (as 3/3 = 1)
3x - 2/(4+x) = 5/3 - 2x
3. Get rid of the fractions:
Multiply each term by (4+x) to get rid of the fraction:
3x(4+x) - 2 = (5/3 - 2x)(4+x)
12x + 3x^2 - 2 = 20 + 5x - 8x^2
4. Simplify the equation:
3x^2 + 12x - 2 = 20 - 3x^2
6x^2 + 12x - 22 = 0
5. Solve the quadratic equation:
Use the quadratic formula to find the roots of the equation:
x = (-b ± √(b^2 - 4ac)) / 2a
x = (-12 ± √(12^2 - 4*6*(-22))) / 2*6
x = (-12 ± √(144 + 528)) / 12
x = (-12 ± √672) / 12
x = (-12 ± 26√3) / 12
6. Check the solution:
Substitute the value of x back into the original equation to check if it satisfies the equation.
Therefore, the solutions to the equation 3x - 2/(4+x) = 2/3 - 2x + 3/3 are x = (-12 + 26√3) / 12 and x = (-12 - 26√3) / 12.
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Solve the following equations using transposition method and check the solution the question is 3 x -2/4+x=2/3-2x+3/3?
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Solve the following equations using transposition method and check the solution the question is 3 x -2/4+x=2/3-2x+3/3? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Solve the following equations using transposition method and check the solution the question is 3 x -2/4+x=2/3-2x+3/3? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Solve the following equations using transposition method and check the solution the question is 3 x -2/4+x=2/3-2x+3/3?.
Solve the following equations using transposition method and check the solution the question is 3 x -2/4+x=2/3-2x+3/3? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Solve the following equations using transposition method and check the solution the question is 3 x -2/4+x=2/3-2x+3/3? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Solve the following equations using transposition method and check the solution the question is 3 x -2/4+x=2/3-2x+3/3?.
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