Question

find value of a^3+27b^3 , if a-2b = -6 and ab=-10 ​

Answer 1

Answer:

324

Step-by-step explanation:

a−3b=−6

Squaring both sides,

=>(a−3b)2=−62

=>a2+9b2−2(a)(3b)=36

=>a2+9b2−6(ab)=36

=>a2+9b2−6(−10)=36

=>a2+9b2=36−60

=>a2+9b2=−24

Now,

a3−(3b)3=(a−3b)[(a)2+(3b)2+(a)(3b)]

a3−27b3=−6(−24+3(−10))

                   =−6(−24−30)

                    =324

Answer 2

Correct Question

Find value of $a^{3} +27b^{3}$ , if $a-3b=-6$   and $ab=-10$

Answer:

The value of $a^{3} +27b^{3}$ is 324.

Step-by-step explanation:

Given:

$a-3b=-6$

$ab=-10$

To Find:

The value of $a^{3} +27b^{3}$.

Formula Used:

$(x-y)^{3} =x^{2} +x^{2} -3xy(x-y)$

Solution:

As given- $a-3b=-6$   and $ab=-10$.

Applying formula no.01.

$(x-y)^{3} =x^{3} +y^{3} -3xy(x-y)$

Putting x=a  and y=3$(a-3b)^{3} =a^{3} +(3b)^{3} -3\times a\times 3b(a-3b)$b in  above formula.

$(a-3b)^{3} =a^{3} +(3b)^{3} -3\times a\times 3b(a-3b)$

$(a-3b)^{3} =a^{3} +27b^{3} -9ab(a-3b)$

Putting the value of  $a-3b=-6$   and $ab=-10$.

$(-6)^{3} =a^{3} +27b^{3} -9(-10)(-6)$

$-216=a^{3} +27b^{3} -540$

$a^{3} +27b^{3}= 540-216$

$a^{3} +27b^{3}= 324$

Thus, the value of  $a^{3} +27b^{3}$  is 324.

PROJECT CODE#SPJ2