The two numbers whose product is 10 and whose sum is 7 are 5 and 2.
Let the two numbers required be x and y.
If the product of the two numbers is 10, then:
xy = 10 ...... 1
If the sum of the numbers is 7, then:
x + y = 7.... 2
Solve both equations simultaneously
From equation 2,
y = 7-x ... 3
Substitute equation 3 into 1 to have:
x(7-x) = 10
Expand
7x - x² = 10
Rearrange in standard form
x² - 7x + 10 = 0
Factorize
x² - 5x - 2x + 10 = 0
x(x-5)-2(x-5) = 0
(x -5)(x-2) =0
x - 5 = 0 and x - 2 = 0
x = 5 and 2
If x = 5:
y = 7 - 5
y = 2
Hence the two numbers whose product is 10 and whose sum is 7 are 5 and 2.
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