Question

if ab =5 and A-b =2 then find the values of a³-b³ answer this ​

Answer 1

Answer:

Step-by-step explanation:

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Answer 2

$\mathfrak{\large{\underline{\underline{Answer:-}}}}$

$\boxed{\bf{a^3 - b^3 = 38}}$

$\mathfrak{\large{\underline{\underline{Explanation:-}}}}$

Given :- ab = 5

a - b = 2

To find : a³ - b³

Solution :-

a - b = 2

By cubing on both the sides

(a - b)³ = 2³

We know that, (x - y)³ = x³ - y³ - 3xy(x - y)

Here x = a , y = b

By substituting the values in the identity we have,

a³ - b³ - 3ab(a - b) = 8

a³ - b³ - 3(5)(2) = 8

[Since a - b = 2 , ab = 5]

a³ - b³ - 30 = 8

a³ - b³ = 8 + 30

a³ - b³ = 38

$\boxed{\bf{a^3 - b^3 = 38}}$

$\mathfrak{\large{\underline{\underline{Identity\:Used:-}}}}$

(x - y)³ = x³ - y³ - 3xy(x - y)

$\mathfrak{\large{\underline{\underline{Some\:Important\:Identities:-}}}}$

[1] (x + y)² = x² + y² + 2xy

[2] (x - y)² = x² + y² - 2xy

[3] (x + y)(x - y) = x² - y²

[4] (x + a)(x + b) = x² + (a + b)x + ab