find the value for expansion question for std 9
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4 ; 52 ; 2702
Step-by-step explanation:
⇒ a = 1 / ( 4 - a )
⇒ ( 4 - a ) = 1 / a
⇒ 4 - a = 1 / a
⇒ 4 = a + 1 / a
Cube on both sides:
⇒ ( a + 1 / a )^3 = 4^3
⇒ a^3 + 1 / a^3 + 3( a * 1 / a )( a + 1 / a ) = 64
⇒ a^3 + 1 / a^3 + 3( a + 1 / a ) = 64
⇒ a^3 + 1 / a^3 + 3( 4 ) = 64
⇒ a^3 + 1 / a^3 + 12 = 64
⇒ a^3 + 1 / a^3 = 64 - 12 = 52
Square on both sides:
⇒ ( a^3 + 1 / a^3 )^2 = 52^2
⇒ a^6 + 1 / a^6 + 2( a^3 * 1 / a^3 ) = 2704
⇒ a^6 + 1 / a^6 + 2( 1 ) = 2704
⇒ a^6 + 1 / a^6 = 2704 - 2 = 2702
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