Question

The sum of two numbers is 90 and the product is 2009. If one number is (45+x). What are the

numbers?​

Answer 1

Answer:

$given \: that \:first \: number \: is \: 45 + x \\given \: sum \: of \: two \: numbers \: is \: 90 \\ then \: the \: second \: number \: is \: 90 - (45 + x) \\ = 45 - x \\ given \: product \: of \: two \: numbers \: is \: 2009 \\ therefore \\ (45 + x)(45 - x) = 2009 \\ (x+ y)(x - y) = {x}^{2} - {y}^{2} \\ {45}^{2} - {x}^{2} = 2009 \\ 2025 - {x}^{2} = 2009 \\ 2025 - 2009 = {x}^{2} \\ 16 = {x}^{2} \\ x = +4 \: or \: - 4 \\ the \: two \: numbers \: are \: 45 - 4 \: and \: 45 + 4\\ i.e \: 41 \: and \: 49$

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