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The values of x in the equation 7(x+2p)2 + 5p2 = 35xp + 117p2 are
- a)(4p, –3p)
- b)(4p, 3p)
- c)(–4p, 3p)
- d)(–4p, –3p)
Correct answer is option 'A'. Can you explain this answer?
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The values of x in the equation 7(x+2p)2 + 5p2 = 35xp + 117p2 area)(4p...
Solution:
The given equation is 7(x - 2p)^2 + 5p^2 = 35xp + 117p^2.
We need to find the values of x that satisfy this equation.
Expanding the square term on the left side, we get:
7(x^2 - 4px + 4p^2) + 5p^2 = 35xp + 117p^2
Simplifying this equation, we get:
7x^2 - 28px + 28p^2 + 5p^2 = 35xp + 117p^2
7x^2 - 35xp + 33p^2 = 0
Dividing both sides by p^2 (since p cannot be zero), we get:
7(x/p)^2 - 35(x/p) + 33 = 0
This is a quadratic equation in (x/p), which we can solve using the quadratic formula:
x/p = [35 ± sqrt(35^2 - 4(7)(33))] / (2*7)
x/p = [35 ± sqrt(961)] / 14
x/p = [35 ± 31] / 14
x/p = 6/14 or 66/14
x = (6/14)p or (66/14)p
Simplifying these expressions, we get:
x = (3/7)p or (33/7)p
Therefore, the values of x that satisfy the given equation are:
x = (3/7)p or (33/7)p.
Hence, option 'A' is the correct answer.
The given equation is 7(x - 2p)^2 + 5p^2 = 35xp + 117p^2.
We need to find the values of x that satisfy this equation.
Expanding the square term on the left side, we get:
7(x^2 - 4px + 4p^2) + 5p^2 = 35xp + 117p^2
Simplifying this equation, we get:
7x^2 - 28px + 28p^2 + 5p^2 = 35xp + 117p^2
7x^2 - 35xp + 33p^2 = 0
Dividing both sides by p^2 (since p cannot be zero), we get:
7(x/p)^2 - 35(x/p) + 33 = 0
This is a quadratic equation in (x/p), which we can solve using the quadratic formula:
x/p = [35 ± sqrt(35^2 - 4(7)(33))] / (2*7)
x/p = [35 ± sqrt(961)] / 14
x/p = [35 ± 31] / 14
x/p = 6/14 or 66/14
x = (6/14)p or (66/14)p
Simplifying these expressions, we get:
x = (3/7)p or (33/7)p
Therefore, the values of x that satisfy the given equation are:
x = (3/7)p or (33/7)p.
Hence, option 'A' is the correct answer.
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