Question

8. Find x
Find x3 – y3 , if x - y = 5 and xy = 14.​

Answer 1

Answer:

x =7

x3 - y3 =335

Step-by-step explanation:

x - y = 5 n xy = 14

then,

xy = 14

=>x = 14/y

then, x-y=5

=> 14/y - y = 5

=> y2 + 5y -14 = 0

now solving this

y = 2

so x-y=5

=>x= 7

Answer 2

Question :-

• $\sf{Find~x^3 - y^3,~if~x - y~=~5~and~xy~=~14}$

Solution :-

Cubing both sides

$\implies\sf{({x - y})^{3} = ({5})^{3}}$

$\bold{by \: using \: this \: identity} \: \implies \\ \boxed{\sf{{(a - b})^{3} = {a}^{3} - {b}^{3} - 3ab(a - b)}}$

$\implies\sf { {x}^{3} - {y}^{3} - 3xy(x - y) = 125}$

$\sf{{x}^{3} - {y}^{3} - 3 \times (14 )\times (5) = 125}$

$\sf{{x}^{3} - {y}^{3} - 210 = 125}$

$\sf{{x}^{3} - {y}^{3}} = 125 + 210$

$\sf{{x}^{3} - {y}^{3}} = 335$

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Know more

• Some useful identities :-
• $\boxed{a + b)^2 = a^2 + b^2 + 2ab}$
• $\boxed{(a - b)^2 = a^2 + b^2 - 2ab}$
• $\boxed{(a + b)^3 = a^3 + b^3 + 3ab(a + b)}$