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Chapter 9: Q. 195 (page 919)

The product of two consecutive odd numbers is 255. Find the numbers.

Short Answer

Expert verified

The odd consecutive numbers whose product is 255 is 15, 17 and-15,-17.

Step by step solution

01

Step 1. Given information.

There are two consecutive odd numbers. Its product is 255.

Find theses numbers using quadratic equation.

02

Step 2. Calculation.

Consider first odd number is x. So the second consecutive odd number is x+2.

So the equation becomes xx+2=255.

x2+2x-255=0

Solve the equation.

localid="1645095963565" x2-15x+17x-255=0xx-15+17x-15=0x-15x+17=0

Now,

localid="1645095983310" x-15=0⇒x=15

localid="1645096004894" x+17=0⇒x=-17

03

Step 3. Conclusion.

  • If the first odd number is 15 then the second odd number is 17.
  • If the First odd number is -15 then the second number is -17.

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