Hello from MrBillDoesMath!
Answer:
11
Discussion:
Let "n" be the smaller number. Then
n * (n+5) = 176.
My first reaction to this problem was to factor 176 in my head. That's 176 = 16 * 11 and 16 is 5 more than 11. So that's the solution!.... Now let's solve it using the brute force approach:
n(n+5) = 176 =>
n^2 + 5n - 176 = 0 => use the quadratic formula
n = ( -5 +\- sqrt( 5^2 - 4(1)(-176)) ) /2
= ( -5 +\- sqrt( 25 + 704) )/ 2
= ( -5 +\- sqrt (729) ) /2 => as sqrt(729) = 27
= (-5 +\- 27) / 2 =>
= (-5 + 27)/2 or ( -5 -27)/2 =>
= 22/2 or -32/2 =>
= 11 or -16
But -16 is not allowed as the question wants a positive value.
Thank you,
MrB
Answer:
11
Step-by-step explanation:
let x be the smaller number.
from question statement,we get
x(x+5)=176
x²+5x=176
adding -176 in both sides of equation,we get
x²+5x-176=176-176
x²+5x-176=0
by factorization, split the middle term to make the equation into such that the sum of two numbers should be 5 and their product be -176.
x²+16x-11x-176=0
Making two groups and taking the common out:
x(x+16)-11(x+16)=0
(x+16)(x-11)=0
either x+16=0 or x-11=0
either x=-16 or x=11.
-16 is not positive. so, 11 is the smaller number.
