Question

Find the value of p³-q³ , if p- q = 10/9 and pq = 5/3.​

Answer 1

Answer:

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Step-by-step explanation:

p-q = 10/9

cubing on both sides

(p-q)³ = (10/9)³

p³-q³- 3pq (p-q) = 1000/729

p³-q³- 3× (5/3) × (10/9) = 1000/729

p³-q³- 50/9 = 1000/729

p³-q³ = 1000/729 + 50/9

p³-q³ = (1000+405) / 729

p³-q³ = 1405/729

= 1.93

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Answer 2

${ \tt{ \red{ \underline{GIVEN- }}}}$



${ \sf{ \blue{p - q = \frac{10}{9}}}}$



${ \sf{ \blue{pq = \frac{5}{3}}}}$



${ \red{ \underline{ \tt{TO \: FIND- }}}}$



${ \rightarrow{ \sf{\green{ {p}^{3} - {q}^{3}}}} }$



${ \red{ \tt{ \underline{ Solution-}}}}$



▪ using the algebraic identity given below...



${ \boxed{ \boxed{ \sf{ \pink{ {a}^{3} - {b}^{3} = (a - b)( {a}^{2} + {b}^{2} +ab)}}}}}$



now, at first we have to find the value of



${ \sf{ \rightarrow{ {p}^{2} + {q}^{2} }}}$



▪ we know that...



${ \boxed{ \boxed{ \sf{ \pink{ {(a - b)}^{2} = {a}^{2} + {b}^{2} - 2ab}}}}}$



using this formula...



${ \sf{ \rightarrow{ {(p - q)}^{2} = {p}^{2} + {q}^{2} - 2pq}}}$



${ \sf{ \implies{( { \frac{10}{9}) }^{2} = {p}^{2} + {q}^{2} - (2 \times \frac{5}{3})}}}$




${ \sf{ \implies{ \frac{100}{81} = {p}^{2} + {q}^{2} - \frac{10}{3}}}}$



${ \implies{ \sf{ {p}^{2} + {q}^{2} = \frac{100}{81} + \frac{10}{3}}}}$



${ \sf{ \implies{ {p}^{2} + {q}^{2} = \frac{100 + (10 \times 27)}{81}}}}$



${ \sf{ \implies{ {p}^{2} + {q}^{2} = \frac{100 + 270}{81}}}}$



${ \sf{ \implies{ {p}^{2} + {q}^{2} = \frac{370}{81}}}}$



${ \red{ \sf{ {p }^3-{ q}^{3} = (p - q)( {p}^{2} + {q}^{2} + pq)}}}$



now, putting this value in the first formula mentioned above...



${ \implies{ \sf{ {p }^3-{ q}^{3} = \frac{10}{9} ( \frac{370}{81} + \frac{5}{3} )}}}$



${ \implies{ \sf{ {p}^3 -{ q}^{3} = \frac{10}{9} ( \frac{370}{81} + \frac{5}{3} )}}}$



${ \implies{ \sf{ {p }^3- {q}^{3} = \frac{10}{9} ( \frac{370 +(5 \times 27)}{81} )}}}$



${ \implies{ \sf{ {p }^3-{ q}^{3} = \frac{10}{9} ( \frac{370 +135}{81} )}}}$



${ \implies{ \sf{ {p}^3 -{ q}^{3} = \frac{10}{9} \times \frac{505}{81} }}}$



${ \implies{ \underline{ \boxed{ \sf{ \red{ {p}^3 -{ q}^{3} = \frac{5050}{729}}}}}}}$