What should be the number added to the 5x^2 - 6x +9 then obtain 2x^2-5x+4
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Given: The numbers (5x + 2), (4x - 1) and (x + 2) are in AP.
To find: The value of x.
Solution:
Let a1 = (5x + 2)
a2 = 4x - 1)
a3 = (x + 2)
Since, the terms are in an AP, therefore common difference is same.
⇒ a2 - a1 = a3 - a2
⇒(4x - 1) - (5x + 2) = (x + 2) - (4x - 1)
⇒ 4x - 1 - 5x - 2 = x + 2 - 4x +1
⇒ - x - 3 = - 3x + 3
⇒ -x + 3x = 3 + 3
⇒ 2x = 6
⇒ x = 3
∴ x = 3
To find: The value of x.
Solution:
Let a1 = (5x + 2)
a2 = 4x - 1)
a3 = (x + 2)
Since, the terms are in an AP, therefore common difference is same.
⇒ a2 - a1 = a3 - a2
⇒(4x - 1) - (5x + 2) = (x + 2) - (4x - 1)
⇒ 4x - 1 - 5x - 2 = x + 2 - 4x +1
⇒ - x - 3 = - 3x + 3
⇒ -x + 3x = 3 + 3
⇒ 2x = 6
⇒ x = 3
∴ x = 3
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