Math, asked by asl23, 1 year ago

p3-q3 if p-q=10/9 , pq=5/3

Answers

Answered by hukam0685
12

\bf {p}^{3}  -  {q}^{3}   =6.93 \\

Given:

  • p - q =  \frac{10}{9} ...eq1 \\ and
  • pq =  \frac{5}{3}...eq2  \\

To find:

  • Find the value of  {p}^{3}  -  {q}^{3}  \\

Solution:

Identity to be used:

\bf ( {x - y)}^{3} =   {x}^{3}  -  {y}^{3}  - 3xy(x - y) \\

Step 1:

Take cube of eq1.

( {p - q)}^{3 }  = \left( { \frac{10}{9} }\right)^{3}  \\

Apply identity.

  {p}^{3}  -  {q}^{3}  - 3pq(p - q)  =  \frac{1000}{729}...eq3 \\

Step 2:

Put value from eq1 and eq2 in eq3.

 {p}^{3}  -  {q}^{3}  - 3 \times  \frac{5}{3} ( \frac{10}{9} )  =  \frac{1000}{729} \\

or

{p}^{3}  -  {q}^{3}  - \frac{50}{9}  =  \frac{1000}{729} \\

or

{p}^{3}  -  {q}^{3}   =  \frac{1000}{729} + \frac{50}{9}\\

or

{p}^{3}  -  {q}^{3}   =  \frac{1000 + 50 \times 81}{729} \\

or

{p}^{3}  -  {q}^{3}   =  \frac{5050}{729} \\

or

{p}^{3}  -  {q}^{3}   =6.93 \\

Thus,

\bf {p}^{3}  -  {q}^{3}   =6.93 \\

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