-7. be real numbers with a 20 and let a, be the roots of the equation ax + bx +C the roots of a x2 + abcx + C = 0 in terms of a, B O Express to learn the Bare roots of X -- px + 9 = 0 and a-2. B + 2 are roots of x-px 169 + (r + 4 - 9) = 4p?. are roots of *+9=0 and a -2,8 + 2 are rots et o then prove that A-9. If one root of the equation ax2 + bx + C = 0 is equal to nth power of the other root, then show that (ach) 1/(n + 1) + (alc)/n+1) + b = 0.

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Let One wot be ( alpha ). ( Rightarrow ) 2nd ( n=alpha^{n} ) Its a question on sheet ( therefore quad alpha cdot alpha^{n}=frac{c}{a} ) ( Rightarrow quad alpha^{n+1}=frac{c}{a} ) ( therefore quad alpha=left(frac{c}{9}right)^{1 / n+1} ) ( therefore a cdotleft(frac{c}{a}right)^{frac{2}{n+1}}+b cdotleft(frac{c}{a}right)^{frac{1}{n+1}}+c=0 ) ( Rightarrow a^{1-frac{2}{n-1}} cdot c^{n+1}+b cdot frac{c^{frac{2}{n+1}}}{a^{frac{1}{n+1}}}+c=0 ) ( Rightarrow a^{frac{n-1}{n+1}} cdot c^{frac{2}{n+1}+b}+cdots+c=0 ) ( n ) ( Rightarrow quad a^{frac{n}{n+1}} cdot c^{frac{2}{n+1}}+b cdot c^{frac{1}{n+1}}+c=0 ) ( y ) ( left.zleft(a^{n} cright)^{frac{1}{n+1}+left(a c^{n}right)^{(n+1}+b=0}right) )

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