Question

if a-b =10,ab=25,find the values of a3-b3

Answer 1

heya mate hope this helps u

Answer 2

Solution:

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Given:

a - b = 10,

ab = 25,.

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To find:

The value of a³ - b³

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As, we know that,

(a - b)² = a² + 2ab + b²


=> a - b = 10,.

=> (a - b)² = (10)²

=> a² - 2ab + b² = 100

=> a² - 2(25) + b² = 100

=> a² - 50 + b² = 100

=> a² + b² = 100+50

=> a² + b² = 150,.....(ii),.

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We know that,

(a + b)² = a² + 2ab + b²

=> (a + b)²

=> a² + 2ab + b²

=> 150 + 2(25)

=> 150 + 50

=> 200

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=> (a + b)² = 200

=> a + b = 10√2 ...(iii)


Adding (i) & (ii), we get,

=>  a + b + a - b = 10 + 10√2

=> 2a =  10 (√2 + 1)

=> a = 5(√2 + 1),...

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=> a + b = 10√2

=> 5√2 + 5 + b = 10√2

=> 5 + b = 10√2 - 5√2

=> 5 + b = 5√2

=> b = 5√2 - 5

=> b = 5(√2 - 1)

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We know that,

=> a³ - b³ = (a + b)(a² - ab + b²)

=> (5(√2+1) + 5(√2 -1))((5(√2 -1))² - 25 + (5(√2 - 1))²)

=> (5(√2 + 1 - √2 +1))(25(2 + 1 -2√2) - 25 + 25(2 +1 + 2√2))

=> 5 (2)( 25 ( 3 - 2√2) - 25 + 25 (3 - 2√2)

=> 5(2)( 25 (3 - 2√2 + 3 + 2√2 + 1)

=> 10(25(7))

=> 10 (175)

=> 1750,..

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                               Hope it Helps!!

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