Question

If the equation 9x^2+(27*3^1/p)x+4=0 has equal roots then prove that p=-1/2

Answer 1

"mn=−9+81−24 −−−−−− √−9−81−24 −−−−−− √mn=−9+81−24−9−81−24

=9−57−−√9+57 −− √=(9−57 −− √)281−57=9−579+57=(9−57)281−57

= (9−57−−√)224=(9−57)224

mn−−−√=9−57−−√26–√mn=9−5726

nm−−−√=9+57−−√26–√nm=9+5726

Adding it

Answer = 332 −− √

Let ma and na are the roots of 3x^2+9x+2=0

ma+na =-9/3

(m+n).a = -3

A = -3/(m+n) ……………………..(1)

ma.na = 2/3

m.n.a^2 = 2/3

put a = -3/(m+n) from eq. (1)

m.n.9/ (m+n)^2=2/3

(m+n)^2=27.m.n/2

(m+n)=+/-3(3/2)^ 1/2.(m.n)^1/2

(m+n)/(m.n)^1/2= +/-(3/2).(6)^1/2

M/(m.n)^1/2 + n /(m.n)^1/2=+/-(3/2). (6)^1/2

(M/n)^1/2+ (n/m) ^1/2= +/-(3/2).(6)^1/2 , Answer

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