Free help with homework

Why join Brainly?

  • ask questions about your assignment
  • get answers with explanations
  • find similar questions



This Is a Certified Answer

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
The geometric mean is similar to the arithmetic mean (or average). The geometric mean of n terms is equal to the nth root of the n terms or :
GM= \sqrt[n]{a_1a_2a_3...a_n}

 \sqrt{2x(19x-2)} =7x-2\\ \sqrt{38x^2-4x} =7x-2 \\ 38x^2-4x=49x^2-28x+4 \\ 0=11x^2-24x+4 \\ 0=(11x-2)(x-2)

So x can be equal to 2 or 2/11. We check if these are extraneous roots (meaning they do not work).

When x = 2,
 \sqrt{2(2)(19*2-2)} =7(2)-2 \\  \sqrt{4(36)}=12 \\ 12=12
This is true therefore x can be 2.

When x = 2/11
 \sqrt{2( \frac{2}{11})(19* \frac{2}{11} -2 )}=7( \frac{2}{11}  )-2 \\  \sqrt{ \frac{4}{11}( \frac{16}{11})  } = -\frac{8}{11}  \\  \frac{8}{11} = -\frac{8}{11}
This is not true therefore x cannot be 2/11.

The only possible value of x is then 2.

0 0 0
The Brain
  • The Brain
  • Helper
Not sure about the answer?
Learn more with Brainly!
Having trouble with your homework?
Get free help!
  • 80% of questions are answered in under 10 minutes
  • Answers come with explanations, so that you can learn
  • Answer quality is ensured by our experts