Question

if 3a+1/2a = 6 find 4a(square) + 1/9a(square)?

Answer 1

Answer:

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Answer 2

Given:

The equation is  $3a+\frac{1}{2a}=6$

To find:

The value of  $4a^{2} +\frac{1}{9a^{2} }$

Solution:

$3a+\frac{1}{2a}=6$ can be written as:

$\frac{6a^{2}+1 }{2a} =6$

6a² + 1 = 12a

6a² - 12a + 1 = 0

Using the quadratic formula, we can get the values of a:

a = (12± √12² - 4*6*1) / 2*6

= (12± √144-24 ) / 12

= (12± √120) / 12

a = 2.080 and -0.080

Putting the value of a = 2.080 in the equation  $4a^{2} +\frac{1}{9a^{2} }$ we get:

4*(2.080)² + 1/ 9*(2.080)²

= 4*4.3264 + 1/ 9*4.3264

= 17.3056 + 0.0257

= 17.3306

Putting the value of a = -0.08 we get:

=4*(0.08)² + 1/ 9*(0.08)2

=4*0.0064 + 1/ 9*0.0064

= 0.0256 + 17.3611

= 17.3867

Therefore the value of the given equation for a = 2.080 will be 17.3306 and for a = -0.08 will be 17.3867.