Question

Find two positive whole numbers that differ by 6 and whose product is 91.​

Answer 1

Step-by-step explanation:

Given:-

two positive whole numbers that differ by 6 and whose product is 91.

To find:-

Find two positive whole numbers that differ by 6 and whose product is 91.

Solution:-

Let the two positive numbers be X and Y

Let X>Y

They differ by 6

=>X-Y=6------(1)

Their product =91

=>XY=91-----(2)

We know that

(a+b)²=(a-b)²+4ab

=>(X+Y)²=(X-Y)²+4XY

=>(X+Y)²=6²+4(91)

=>(X+Y)²=36+364

=>(X+Y)²=400

=>X+Y=√400

=>X+Y=20------(2)

adding (1)&(2)

X+Y=20

X-Y=6

(+)

______

2X+0=26

_______

=>2X=26

=>X=26/2

=>X=13

On Substituting the value of X in (1) then

=>13-Y=6

=>Y=13-6

=>Y=7

Answer:-

The two positive numbers are 13 and 7

Check:-

X=13

Y=7

Their difference=13-7=6

Their product=13×7=91

Verified the given relations

Used formulae:-

• (a+b)²=(a-b)²+4ab