Maths-
General
Easy
Question
If the product of two numbers is 10 and their sum is 7, what is the larger of the two
Numbers?
Hint:
While evaluating the expression just put the values and perform basic operations.
The correct answer is: Hence, the larger number is 5.
Answer:
- Step by step explanation:
○ Given:
Product of number is 10
and the sum of two numbers is 7.
○ Step 1:
○ Let the number be one number be x and another number be y.
○ Given that the product of two numbers is 10.
∴ x y = 10
x =
—------- eqn. 1
○ Given that the sum of two numbers is 7.
∴ x + y = 7 —------- eqn. 2
○ Step 2:
Put x = in equation
x + y = 7
+ y = 7
+ = 7
10 + y2 = 7y
y2 - 7y + 10 = 0
○ Step 3:
Solve quadratic equation by factorization:
y2 - 7y + 10 = 0
y2 - 5y - 2y + 10 = 0
y (y - 5) - 2(y - 5) = 0
(y - 5) (y - 2) = 0
Equate to zero
(y - 5) = 0 y = 5
(y - 2) = 0 y = 2
○ Step 3:
Put y = 5 and y = 2 in x =
x = 
and x = 
x = 2, and x = 5
So, we get numbers 2 and 5.
- Final Answer:
Hence, the larger number is 5.
x = —------- eqn. 1○ Given that the sum of two numbers is 7.
○ Step 2:
in equation + y = 7 + = 710 + y2 = 7yy2 - 7y + 10 = 0○ Step 3:
Solve quadratic equation by factorization:
y2 - 5y - 2y + 10 = 0y (y - 5) - 2(y - 5) = 0(y - 5) (y - 2) = 0 y = 5 y = 2○ Step 3:
x = and x = x = 2, and x = 5So, we get numbers 2 and 5.
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