Answers

2015-11-12T16:04:03+05:30

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.
√a  + b = 11      => b = 11 - √a
7√b + a = 11
 => 49 b = (11 - a)²
 => 539 - 49 √a = (11 - a)²
 => 49 √a = 539 - (11 - a)²
 => 49² a  = 539² + (11 - a)⁴  - 2 * 539 * (11 - a)
 => a⁴ - 4 * 11 a³ + 6 *11² * a² - 4 *11³ a + 11⁴ - 22 * 539 + 1078 a - 49² a = 0
 => P(x) = a⁴ - 44 a³ + 726 a² - 7725 a  + 2783 = 0
 => 
a has four positive real values at most.  It appears.
Two of them are :
      a ≈ 0.37304      and  a ≈ 27.7359
       b ≈ 10.389      and    b ≈ 5.7335

There are no real negative roots.
Perhaps there are two more real positive roots or there are two imaginary roots.

The derivative of P(x) = P'(x) = 4 a³ - 132 a² + 1452 a - 7725
       has  one real root.  and two imaginary roots.
 
So P(x) can have at most two real roots.

The solutions as above are good.


1 5 1
click on thanks button above;;; select best answer