Find two numbers whose sum is 55 and whose product is 684.

unknown values: a,b

equation: a + b = 55

equation: ab = 684

answer: {19; 36}

the sum of two numbers is 8.5 and their product is 18. What are the numbers?

unknown values: x,y

equation: x + y = 8.5

equation: xy = 18

answer: {4; 4.5} | {4; 9/2}

two positive real numbers have a sum of 7 and a product of 11. Find the numbers.

unknown values: x,y

equation: x + y = 7

equation: xy = 11

answer: {2.382; 4.618}

Three numbers are positive consecutive odd integers. If the larger two numbers have a product of 195, find all three integers.

unknown values: 2*k-1,2*k+1,2*k+3

equation: (2*k+1)*(2*k+3)=195

answer: 11; 13; 15

What three consecutive odd numbers have a product of 12075?

unknown values: 2*k-1,2*k+1,2*k+3

equation: (2*k-1)(2*k+1)(2*k+3)=12075

answer: 21; 23; 25

If 18 is decreased by the sum of a number and 6, the result is 4 less than 3 times the number. Find the number

unknown values: x

equation: 18-(x+6)=3*x-4

answer: 4

M is a perfect square of an integer. The next larger perfect square is M + 461. What is M?

unknown values: x^2

equation: x^2+461=(x+1)^2

answer: 52900

The sum of two consecutive odd integers is 236. What is the smaller integer?

unknown values: 2*k-1

equation: (2*k-1)+(2*k+1)=236

answer: 117

find two consecutive odd positive odd numbers which are such that the square of their sum exceeds the sum of their square by 126

unknown values: 2*k-1,2*k+1

equation: (2*k-1)^2+(2*k+1)^2+126=(2*k-1+2*k+1)^2

answer: 7; 9

The sum of two times one number and three times another is 29. The difference between twice the first and the second is 1. Solve algebraically to find the numbers.

unknown values: x,y

equation: 2*x + 3*y = 29

equation: 2*x - y = 1

answer: 4; 7