Question

if 36a^2 -1/9a^2=4 then what is 216a^3-1/27a^3=?​

Answer 1

Answer:

Your answer is 8

Step-by-step explanation:

If 36a^2-1/9a^2=4 because square of 2 is 4

216a^3-1/27a^3= 8 and cube of 2 is 8

Answer 2

Answer:

8.03

Step-by-step explanation:

In the given question,

We have been provided the equation,

$36a^{2}-\frac{1}{9}a^{2}=4$

We need to calculate the value of,

$216a^{3}-\frac{1}{27}a^{3}$

Now,

$36a^{2}-\frac{1}{9}a^{2}=4\\(6a)^{2}-(\frac{1}{3}a)^{2}=(2)^{2}\\(6a+\frac{a}{3})(6a-\frac{a}{3})=4\\(\frac{19a}{3})(\frac{17a}{3})=4\\So,\\a^{2}=\frac{36}{323}$

Now,

We need to calculate this,

$216a^{3}-\frac{1}{27}a^{3}=(6a)^{3}-(\frac{1}{3}a)^{3}\\(6a)^{3}-(\frac{1}{3}a)^{3}=(6a-\frac{a}{3})(36a^{2}+2a^{2}+\frac{a^{2}}{9})\\=(\frac{17a}{3})(36a^{2}+2a^{2}+\frac{a^{2}}{9})$

Now, on putting the value of $a^{2}$ from above in this we get,

$(\frac{17a}{3})(36(\frac{36}{323})+2(\frac{36}{323})+(\frac{36}{323\times 9}))\\=(\frac{17a}{3})(\frac{11664+648+36}{323\times 9})\\=4.2476\times1.8918\\=8.03$

This is obtained by putting the value of $a^{2}$ and the value of 'a' from the above equation,

Therefore, the value of the given equation is 8.03