x এর সকল মানের জন্য (ax +২) (bx +৭) =১৫ +cx +১৪ এবং a+b =৮ হলে, c এর মান কত হতে পারে?
Created: 4 years ago |
Updated: 3 years ago
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Given,
(ax + 2) (bx + 7) = 15x^2 + cx + 14
abx^2 + 7ax + 2bx + 14 = 15x^2 + cx + 14
abx^2 + (7a + 2b) x + 14 = 15x^2 + cx + 14
Comparing on both sides,
ab = 15 (7a + 2b) = c
And already given a + b = 8
We know that (a - b) ^2 = (a + b) ^2 - 4ab
(a - b) ^2 = (8) ^2 - 4(15)
(a - b) ^2 = 64 – 60
(a - b) ^2 = 4
(a - b) = √4
(a - b) = + 2 or (a - b) = - 2
Case 1: a - b = 2
a + b = 8→eq1
a - b = 2→eq2
Solving these two we get
2a = 10
a = 5
By substituting a value in eq1
5 + b = 8
b = 3
As c = (7a + 2b)
c = (7(5) + 2(3))
c = 41.
Case 2 :a - b = - 2
a + b = 8
a - b = - 2
Solving these two equations we get
2a = 6
a = 3
By substituting a value in eq1
3 + b = 8
b = 5
As c = (7a + 2b)
c = (7(3) + 2(5))
c = 31.
So the two possible values of c are 41 and 31.
(ax + 2) (bx + 7) = 15x^2 + cx + 14
abx^2 + 7ax + 2bx + 14 = 15x^2 + cx + 14
abx^2 + (7a + 2b) x + 14 = 15x^2 + cx + 14
Comparing on both sides,
ab = 15 (7a + 2b) = c
And already given a + b = 8
We know that (a - b) ^2 = (a + b) ^2 - 4ab
(a - b) ^2 = (8) ^2 - 4(15)
(a - b) ^2 = 64 – 60
(a - b) ^2 = 4
(a - b) = √4
(a - b) = + 2 or (a - b) = - 2
Case 1: a - b = 2
a + b = 8→eq1
a - b = 2→eq2
Solving these two we get
2a = 10
a = 5
By substituting a value in eq1
5 + b = 8
b = 3
As c = (7a + 2b)
c = (7(5) + 2(3))
c = 41.
Case 2 :a - b = - 2
a + b = 8
a - b = - 2
Solving these two equations we get
2a = 6
a = 3
By substituting a value in eq1
3 + b = 8
b = 5
As c = (7a + 2b)
c = (7(3) + 2(5))
c = 31.
So the two possible values of c are 41 and 31.
Md Azizur Rahman
Founder of Satt
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