Question

solve asap 6.2 not 6.1

Answer 1

may be ans z - 1/2√3

Answer 2

let the present age of son be x
∴present age of the father =x²
∴after some years age of son =x²/2
∴after some yers age of father =8x
let their ages will satisfy the given conditions after y years.
as per condition
y=8x-x².......(1)
as per second condition
y=x²/2 -x.......(2)
equating (1)and (2)
8x-x²=x²/2 -x
8x- x²=(x²-2x)/2
16x-2x²=x²-2x
3x²=18x
x²=6x
x²-6x=0
x(x-6)=0
∴either x=0
or x-6=0
x=6
x=6 is acceptable [∵age must be a natural number]
∴the present age of father is x²=36

[N.B -while solving the problem always keep in mind that while solving an equation we can not cancel its variable.that is why we have not cancelled x although we could have cancelled it when we got the equation 3x²=18x . though here would have been no change in the answer if we had cancelled x since we were dealing with ages but if the conditions were different then we might have missed a possible value for x i.e x=0]