(a) The difference of the squares of two natural numbers is 84. The square of the larger number is 25 times the smaller number. Find the numbers. [4]
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x^2 - y^2 = 84
let x > y
so x^2 = 25y
25y-y^2= 84
25y - y^2 -84 = 0
this can be written as,
y^2 - 21y - 4y + 84 = 0
using middle term splitting
y(y-21) - 4 (y - 21) =0
(y-21)(y-4)=0
y = either 21 or 4
x= either root (25*21) or root (25 * 4) (which is 10)
let x > y
so x^2 = 25y
25y-y^2= 84
25y - y^2 -84 = 0
this can be written as,
y^2 - 21y - 4y + 84 = 0
using middle term splitting
y(y-21) - 4 (y - 21) =0
(y-21)(y-4)=0
y = either 21 or 4
x= either root (25*21) or root (25 * 4) (which is 10)
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