If the sum of the roots of the quadratic equation ax square + bx + c = 0 is equal to the sum of the cubes of their reciprocals, then prove that ab square = 3a square c + c cube.
Answers
Answered by
12
✨HERE IS YOUR ANS✨
☺EQUATION - ax²+bx+c = 0
◾ let roots of the equation will be = M &Q
M+Q = -b/a
MQ. = c/a
given that -
(1/M)³+(1/Q)³= M+Q
Q³+M³/(MQ)³ = -b/a
-b³+3abc/a³/c³/a³ = -b/a
-b³+3abc/c³=-b/a
(b²-3ac )/c³ = 1/a
by cross multiply -
ab² -3a²c = c³
[ab² = c³ + 3a²c ]
henc proved//.
hope it helps u
☺EQUATION - ax²+bx+c = 0
◾ let roots of the equation will be = M &Q
M+Q = -b/a
MQ. = c/a
given that -
(1/M)³+(1/Q)³= M+Q
Q³+M³/(MQ)³ = -b/a
-b³+3abc/a³/c³/a³ = -b/a
-b³+3abc/c³=-b/a
(b²-3ac )/c³ = 1/a
by cross multiply -
ab² -3a²c = c³
[ab² = c³ + 3a²c ]
henc proved//.
hope it helps u
Similar questions