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In $19-25,$ express each answer in simplest radical form. Check each answer. The larger of two numbers is 5 more than twice the smaller. The square of the smaller is equal to the larger. Find the numbers.

$1 \pm \sqrt{6}$ and $7 \pm 2 \sqrt{6}$

Algebra

Chapter 5

QUADRATIC FUNCTIONS AND COMPLEX NUMBERS

Section 2

The Quadratic Formula

Equations and Inequalities

Quadratic Functions

Complex Numbers

Polynomials

Missouri State University

Oregon State University

University of Michigan - Ann Arbor

Lectures

01:32

In mathematics, the absolu…

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03:52

In $19-25,$ express each a…

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Simplify each radical expr…

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Simplify each expression a…

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Determine the smallest num…

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Write each number in simpl…

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Simplify each radical. Ass…

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Write the radical expressi…

this question. Here we have two numbers. Let's call it be a action. Why we can say that? Why is a larger of the two numbers? So we know that the larger of the two numbers why is equal to five more than twice the smaller one. So that's five plus two X. And we know that small square of a smaller number X were is equal to the larger number. So by and we want to find the two numbers Well, if we know that both of these five close to X and X squared are both equal to why we're gonna quite them to each other. So we know that five plus two X is equal to X squared. Then If we subtract two x plus five from both sides of the equation, we got our quadratic equation. X squared minus two X minus five is equal to zero. Now you can use our quadratic formula to solve for what X is equal to so yeah to, or a negative P plus finest square room, a P square minus four a c divided by two way. This is equal to two plus finest square root of 24 over to which is equal to two post minus two Route six over to or one of plus minus root. Six. So that means that actually either equal to one plus Route six or X is equal to one minus route. Six. Well, if X is equal to one plus Route six, we know that why is able to five plus two X? That means that why is equal to five plus two times X, which is to plus 26 or seven plus two. Route six now in excess, equal to one minus root sex wise equal to five plus two minus two. Route six Or why is equal to seven minus two. Route six So you have to situations here when ecstasy goto one plus fruit. Six. Why is he going to seven plus two? Route six and when X is equal to one minus Route six. Why is equal to seven minus two Route six

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