If a+2b=10 and ab=15 then find the value of a cube + 8b cube
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Answered by
6
Given a +2b = 10 and ab = 15
Consider, a^3 + 8b^3 = a^3 + (2b)^3
=(a+2b)^3 − 3 × a × 2b(a + 2b) [Since, a^3 + b^3 = (a + b)− 3ab(a + b)]
= (a + 2b)^3 − 6ab(a + 2b)
= (10)^3 − 6 × 15 × 10
= 1000 − 900 = 100
Consider, a^3 + 8b^3 = a^3 + (2b)^3
=(a+2b)^3 − 3 × a × 2b(a + 2b) [Since, a^3 + b^3 = (a + b)− 3ab(a + b)]
= (a + 2b)^3 − 6ab(a + 2b)
= (10)^3 − 6 × 15 × 10
= 1000 − 900 = 100
Answered by
3
a + 2b = 10
ab = 15
as we know that
( x + y )^3 = x^3 + y^3 + 3xy ( x + y )
so here
( a + 2b )^3 = ( a )^3 + ( 2b )^3 + 3 ( a )( 2b ) ( a + 2b )
10^3 = a^3 + 8b^3 + 6ab ( a + 2b )
1000 = a^3 + 8b^3 + 6 × 15 × 10
1000 = a^3 + 8b^3 + 900
a^3 + 8b^3 = 1000 - 900
a^3 + 8b^3 = 100
ab = 15
as we know that
( x + y )^3 = x^3 + y^3 + 3xy ( x + y )
so here
( a + 2b )^3 = ( a )^3 + ( 2b )^3 + 3 ( a )( 2b ) ( a + 2b )
10^3 = a^3 + 8b^3 + 6ab ( a + 2b )
1000 = a^3 + 8b^3 + 6 × 15 × 10
1000 = a^3 + 8b^3 + 900
a^3 + 8b^3 = 1000 - 900
a^3 + 8b^3 = 100
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