Question

III. Two marks Questions :
The product of two numbers is 91 and their mean is 10, find the two numbers.
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Answer 1

Answer:

13 and 7

Step-by-step explanation:

Let the numbers be x and y

xy = 91

(x + y) / 2 = 10

Therefore, x + y = 20

x = 20 - y

Hence, in the first equation, we substitute x:

(20 - y) y = 91

20y - y^2 = 91

y^2 - 20y + 91 = 0

Solving, the quadratic equation, we get:

y = 13 or y = 7

Hence, x = 91/y, which is either 7 or 13

Answer 2

Answer:

Let one number be x

Other number = 91/x

ATQ (x+91/x)/2=10

therefore x+91/x= 20

Taking LCM

(x^2+91)/x = 20

=> x^2 + 91 = 20x

=> x^-20x+91=0

=> x^+7x+13x+91=0

=>x(x+7)+13(x+7)=0

=>(x+13)(x+7)=0

therefore x can be -13 and -7

checking the answer

lets suppose x is -13

other number = 91/-13= -7

-13-7/2

-20/2

-10

Mean cannot be negative hence 10 is the answer