Question

The product of two number is 2l and diffexno
is 4 then the ratio of the sum of their
cubes to the difference of their cutes is 185:158​

Answer 1

Step-by-step explanation:

Let the number be x and y.

x−y=4

xy=21

x ^3 − y ^3 = (x−y)[x^2 + y^2 + xy −2xy + 2xy]

=(x−y)[(x−y)^2 + 3xy]

=4(16+63)=4×79=316

⇒ squaring on both sides in x−y=4

(x−y)^2=(4)^2

x^2 + y^2 − 2xy = 16

adding 2xy on both sides:

⇒x^2 + y^2 - 2xy + 2xy = 16 + 2xy

⇒(x+y)^2 - 2xy = 16 + 2xy

⇒(x+y)^2 = 16 + 4xy =16+4×21 = 100

⇒ x+y=10

∴x^3 + y^3 =(x+y)[x^2 + y^2 − xy]

=(x+y)(x^2 + y^2 −xy + 2xy − 2xy)

= (10)[(x+y)^2 − 3xy]⇒10(100 − 3 × 21) = 370

Required ratio = (x^3 − y^3) /(x^3 + y^3)

=370 : 316

=185 : 158

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