Question

Convert in quadratic solution: The difference of two digits is 3 und their product is 270 .

Answer 1

Answer:

xy=270

x=270/y. ....... (i)

x-y=3

x=3+y. .........(ii)

270/y=3+y

270=3y+y^2

y^2+3y-270=0

Answer 2

Given - Difference of two digits - 3

Product of two digits - 270

Find - To form quadratic equation using given information.

Solution - Let the two digits be X and y. As per the first statement, X - y = 3. As per the second statement, X*y = 270.

It can also be written as = y = 270/X

Keeping value of y in first equation-

X - 270/X = 3

Multiplying whole equation with X, we get -

x² - 270 = 3x.

x² - 3x - 270 is the required quadratic equation.

Solving quadratic equation -

X = -b +- ✓(b² - 4ac)/2a

X = 3 +- ✓(9 + 1080) /2*1

x = (3 +- 33)/2

X = (3 + 33)/2 X = (3 - 33)/2

X = 18, -15.

Therefore, values of X are 18 and -15 and hence values of y are 21 and -12.