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Question
The sum of two numbers is 22 and the sum of their squares is 404 . the product of two numbers is-
40
44
80
88
ANSWER : 1
Descrption
<p style="margin-left:0px;">Let's denote the two numbers as x and y.</p><p style="margin-left:0px;">According to the given information, we have two equations:</p><ol><li>x + y = 22 (the sum of two numbers is 22).</li><li>x^2 + y^2 = 404 (the sum of their squares is 404).</li></ol><p style="margin-left:0px;">Now, let's find the product of the two numbers, which is xy.</p><p style="margin-left:0px;">We can use the following identity: (x + y)^2 = x^2 + 2xy + y^2</p><p style="margin-left:0px;">We already know that x + y = 22, and we know x^2 + y^2 = 404.</p><p style="margin-left:0px;">So, we can rewrite the identity as: (22)^2 = x^2 + 2xy + 404</p><p style="margin-left:0px;">484 = x^2 + 2xy + 404</p><p style="margin-left:0px;">Now, let's isolate 2xy: 2xy = 484 - 404 2xy = 80</p><p style="margin-left:0px;">Now, divide both sides by 2 to find the product xy: xy = 80 / 2 xy = 40</p><p style="margin-left:0px;">So, the product of the two numbers x and y is 40. The correct answer is 40.</p>
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