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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 11: Q. 197E (page 1069)

The product of two consecutive even numbers is 624. Find the numbers.

Short Answer

Expert verified

Two consecutive even integers whose product is 624 are $26, 24$ and $- 24, - 26$ .

Step by step solution

01

Step 1. Given information

There are two consecutive even numbers. Its product is 624.

Find these numbers using the quadratic equation.

02

Step 2. Calculation

Consider first even number is x. So, the second consecutive even number is $x + 2$ .

So, the equation becomes,

$x (x + 2) = 624 x^{2} + 2 x - 624 = 0$

Solve the equation

$(x - 24) (x + 26) = 0$

So,

$x - 24 = 0 \Rightarrow x = 24$

$x + 26 = 0 \Rightarrow x = - 26$

03

Step 3. Conclusion

If the first even number is 24 then the second even number is 26.
If the first even number is -26 then the second even number is -24.

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Most popular questions from this chapter

Solve $16 y^{2} = 32 y^{3} + 2 y$

Simplify

(a) ${(\frac{1}{2} y^{2})}^{3} {(\frac{2}{3} y)}^{2}$

(b) ${(\frac{1}{2} j^{2})}^{5} {(\frac{2}{5} j^{3})}^{2}$

Simplify-

(a) $\sqrt{75 a^{9}}$

(b) $\sqrt[3]{128 m^{11}}$

(c) $\sqrt[4]{62 n^{7}}$

Multiply : (a) $4 x^{2} (2 x^{2} - 3 x + 5)$

(b) $- 6 a^{3} b (3 a^{2} - 2 a b + 6 b^{2})$

In the following exercise, factor using substitution.

${(x - 3)}^{2} - 5 (x - 3) - 36$

See all solutions

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