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Answers
At present...
My son's age is x.
Two years ago...
My son's age was x - 2.
My age was (x - 2)9/2. [4 and 1/2 can be written as 9/2]
I can also say that it was 9x/2 - 9.
∵ (x - 2)9/2 = (9x - 18)/2 = 9x/2 - 9.
Six years ago...
My son's age was x - 6.
My age was 2(x - 6)².
But, my age at this time was four lesser than my age at two years before, i.e., 4 lesser than 9x/2 - 9, which results in 9x/2 - 13.
So,
2(x - 6)² = 9x/2 - 13
⇒ 2(x² - 12x + 36) = (9x - 26)/2
⇒ 2x² - 24x + 72 = (9x - 26)/2
⇒ 2(2x² - 24x + 72) = 2((9x - 26)/2)
⇒ 4x² - 48x + 144 = 9x - 26
⇒ 4x² - 48x + 144 - 9x + 26 = 0
⇒ 4x² - 57x + 170 = 0
⇒ 4x² - 40x - 17x + 170 = 0
⇒ 4x(x - 10) - 17(x - 10) = 0
⇒ (4x - 17)(x - 10) = 0
Thus my son's age is either 17/4 or 10.
But I assumed of a natural number. So 17/4 can't be, can it?
So my son's age is 10 now.
And my age is 38 now.
Yes, you got it!!!
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