Question

The difference of two numbers is 2,and their product is 80. What numbers are they?

Answer 1

Answer:

let the number be y

therefore other number=y+2

(y+2) y= 80

y^2 + 2y -80= 0

-b+-√b^2-4ac/2a= -2 +- √4+320/2

-2+-18/2 = 16/2=8 and -2-18/2 = -20/2= -10

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Answer 2

let two nos. be x and y,

x - y = 2

x= 2 ± y. ... (1)

x * y = 80

Substitute, 'x' from eqn. (1),

2 + y *y = 80

y² = 80 - 2

y² = 78

y = 8.8 (approx.)

Substitute 'y’ from above ,

x =. 2 + 8

x = 10

So, we get x = 10 and y = 8

Verification:

Rule 1 : x - y = 2,

10 - 8 = 2.

Rule 2 : x*y =80

10*8 = 80.

HENCE, PROVED.