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CBSE Class 10 Answered

If α and β are the zeroes of the polynomial x²-x-4 , evaluate: (i)1/α²+1/β²(ii)α-β (iii)1/α⁵+1/β⁵ (iv)α⁴+β⁴
Asked by siddhantjain248 | 09 Jun, 2018, 03:53: PM
answered-by-expert Expert Answer
begin mathsize 16px style straight alpha plus straight beta equals 1 over 1 equals 1 αβ equals negative 4 1 over straight alpha squared plus 1 over straight beta squared equals fraction numerator straight alpha squared plus straight beta squared over denominator open parentheses αβ close parentheses squared end fraction equals fraction numerator open parentheses straight alpha plus straight beta close parentheses squared minus 2 αβ over denominator open parentheses αβ close parentheses squared end fraction open parentheses straight alpha minus straight beta close parentheses squared equals open parentheses straight alpha plus straight beta close parentheses squared minus 4 αβ straight alpha ⁴ plus straight beta ⁴ equals left parenthesis straight alpha ² plus straight beta ² right parenthesis ² minus 2 straight alpha ² straight beta ² 1 over straight alpha to the power of 5 plus 1 over straight beta to the power of 5 equals fraction numerator straight alpha to the power of 5 plus straight beta to the power of 5 over denominator open parentheses αβ close parentheses to the power of 5 end fraction equals fraction numerator open parentheses straight alpha plus straight beta close parentheses squared minus 2 αβ over denominator open parentheses αβ close parentheses squared end fraction straight alpha to the power of 5 plus straight beta to the power of 5 equals open parentheses straight alpha plus straight beta close parentheses to the power of 5 minus 5 αβ left parenthesis straight alpha plus straight beta right parenthesis left parenthesis straight alpha squared plus αβ plus straight beta squared space right parenthesis end style
Answered by Arun | 11 Jun, 2018, 10:54: AM

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