Dear Student , Please find below the solution to the asked query : 5 a) a12-b12=a62-b62=a6+b6 a6-b6 Since x2-y2=x+yx-y=a6+b6 a32-b32=a6+b6 a3+b3 a3-b3=a6+b6 a+b a2-ab+b2 a-b a2+ab+b2 ANS b) x+12 + x+23 +x+35=915 x+1 + 10 x+2 + 6 x+330=915x+15+10x+20+6x+18=27031x+53=27031x=270-5331x=217x=21731=7Value of x is 7 Please ask single query in single thread Hope this information will clear your doubts about the topic If you have any more doubts just ask here on the forum and our experts will try to help you out as soon as possible Regards

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Dear Student ,

Please find below the solution to the asked query :

5 . a) . a^{12} - b^{12} = {(a^{6})}^{2} - {(b^{6})}^{2} = (a^{6} + b^{6}) (a^{6} - b^{6}) (Since x^{2} - y^{2} = (x + y) (x - y)) = (a^{6} + b^{6}) ({(a^{3})}^{2} - {(b^{3})}^{2}) = (a^{6} + b^{6}) (a^{3} + b^{3}) (a^{3} - b^{3}) = (a^{6} + b^{6}) (a + b) (a^{2} - ab + b^{2}) (a - b) (a^{2} + ab + b^{2}) ANS . . . b) . \frac{x + 1}{2} + \frac{x + 2}{3} + \frac{x + 3}{5} = 9 \frac{15 (x + 1) + 10 (x + 2) + 6 (x + 3)}{30} = 9 15 x + 15 + 10 x + 20 + 6 x + 18 = 270 31 x + 53 = 270 31 x = 270 - 53 31 x = 217 x = \frac{217}{31} = 7 Value of x is 7 .

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