3 years ago

Help me find the value of each expression for number 34. and 35. Please!

Mathematics

1 answer:

iris [78.8K]3 years ago

8 0

34.) 36
35.) 10

please mark me as brainliest

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When the sum of \, 528 \, and three times a positive number is subtracted from the square of the number, the result is \, 120. F

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Let $x$ be the unknown number. So, three times that number means $3x$ , and the square of the number is $x^2$

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Then, we have to subtract this number from $x^2$ , so we have

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The result is 120, so the equation is

$x^2 - 3x - 528 = 120 \iff x^2 - 3x - 648 = 0$

This is a quadratic equation, i.e. an equation like $ax^2+bx+c=0$ . These equation can be solved - assuming they have a solution - with the following formula

$x_{1,2} = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$

If you plug the values from your equation, you have

$x_{1,2} = \dfrac{3\pm\sqrt{9-4\cdot(-648)}}{2} = \dfrac{3\pm\sqrt{9+2592}}{2} = \dfrac{3\pm\sqrt{2601}}{2} = \dfrac{3\pm51}{2}$

So, the two solutions would be

$x = \dfrac{3+51}{2} = \dfrac{54}{2} = 27$

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