Question

The difference of two 2 and their product is 80

Answer 1

Step-by-step explanation:

a - b = 2 -------(1)

ab = 80

a + b = √(a - b)² + 4ab

= √(2)² + 4(80)

= √4+320

= √324

a + b = 18 ------(2)

from equation (1) + (2)

2a = 20

a = 10

So , b = 10 - 2 = 8

The numbers are 10 & 8 .

Answer 2

Answer:

Step-by-step explanation:

LET THE TWO NUMBERS BE X AND Y

GIVEN THEIR DIFFERENCE = 2:

X-Y = 2

X= 2+Y...................(1)

GIVEN PRODUCT = 80:

X*Y = 80................(2)

SUBSTITUTING (1) IN(2);

(2+Y)*Y = 80

Y²+2Y = 80

Y²+2Y-80 =0

SOLVING THE QUADRATIC EQUATION

                                                                                              PRODUCT= -80

                                                                                              SUM =2

Y²-8Y+10Y-80=0

Y(Y-8)+10(Y-8)=0

(Y+10)=0;Y=-10 [ NOT POSSIBLE ]

(Y-8)=0;Y=8

THEREFORE Y= 8

X= Y+2 = 10 .

HOPE THIS HELPS.