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CBSE Class 10 Answered

If A and B are roots x^2 - 6x + 4 = 0 then find the value of [(A-2)^16 + (B-6)^8]÷A^8.
Asked by acv27joy | 10 Dec, 2018, 01:16: PM
answered-by-expert Expert Answer
begin mathsize 12px style x squared minus 6 x plus 4 space equals space 0 r o o t s space a r e space A space equals space 3 plus square root of 5 space space a n d space B space equals space 3 minus square root of 5 fraction numerator open parentheses A minus 2 close parentheses to the power of 16 space plus space open parentheses B minus 6 close parentheses to the power of 8 over denominator A to the power of 8 end fraction space equals space fraction numerator open parentheses 1 plus square root of 5 close parentheses to the power of 16 plus open parentheses negative 3 minus square root of 5 close parentheses to the power of 8 over denominator open parentheses 3 plus square root of 5 close parentheses to the power of 8 end fraction L e t space u s space m u l t i p l y space b o t h space d e n o m i n a t o r space a n d space N u m e r a t o r space b y space open parentheses 3 minus square root of 5 close parentheses to the power of 8 H e n c e space fraction numerator open parentheses A minus 2 close parentheses to the power of 16 space plus space open parentheses B minus 6 close parentheses to the power of 8 over denominator A to the power of 8 end fraction space equals space fraction numerator open parentheses 1 plus square root of 5 close parentheses to the power of 16 plus open parentheses negative 3 minus square root of 5 close parentheses to the power of 8 over denominator open parentheses 3 plus square root of 5 close parentheses to the power of 8 end fraction cross times open parentheses 3 minus square root of 5 close parentheses to the power of 8 over open parentheses 3 minus square root of 5 close parentheses to the power of 8 space equals fraction numerator open parentheses 1 plus square root of 5 close parentheses to the power of 16 open parentheses 3 minus square root of 5 close parentheses to the power of 8 space plus space open parentheses 3 plus square root of 5 close parentheses to the power of 8 open parentheses 3 minus square root of 5 close parentheses to the power of 8 over denominator 4 to the power of 8 end fraction space equals space fraction numerator open parentheses 1 plus square root of 5 close parentheses to the power of 8 open square brackets open parentheses 1 plus square root of 5 close parentheses to the power of 8 open parentheses 3 minus square root of 5 close parentheses to the power of 8 close square brackets plus 4 to the power of 8 over denominator 4 to the power of 8 end fraction equals space fraction numerator open parentheses 1 plus square root of 5 close parentheses to the power of 8 open square brackets open parentheses negative 2 plus 2 square root of 5 close parentheses to the power of 8 close square brackets plus 4 to the power of 8 over denominator 4 to the power of 8 end fraction space equals space fraction numerator 2 to the power of 8 open parentheses square root of 5 plus 1 close parentheses to the power of 8 open parentheses square root of 5 minus 1 close parentheses to the power of 8 plus 4 to the power of 8 over denominator 4 to the power of 8 end fraction space equals space fraction numerator 257 cross times 4 to the power of 8 over denominator 4 to the power of 8 end fraction space equals space 257 end style
Answered by Thiyagarajan K | 13 Dec, 2018, 06:45: AM

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