Question

the difference between two positive numbers is 4 and the difference between their cubesi 316 find their product and sum of their squares

Answer 1

let the numbers be x an y

we have. x-y=4 ,x^3-y^3= 316

now,

x-y=4

cubing on both the sides

(x-y)^3=4^3

x^3-y^3-3xy(x-y)=64

316-3xy(4)=64

316-3xy=64/4

316-3xy=16

-3xy=16-316

-3xy=-300

xy=-300/-3

xy=100

now,

x-y=4

(x-y)^2=4^2

x^2+y^2-2xy=16

x^2+y^2-2*100=16

x^2+y^2-200=16

x^2+y^2=16 +200

x^2+y^2=216

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