Question

if alpha, beta, gama are the roots of x³-2x²+3x-4=0 then the value of alpha square beta square +beta²gama²+gama²alpha² is​

Answer 1

Step-by-step explanation:

Here is your answer please mark Brainlest

Answer 2

x³-2x²+3x-4=0

a=1 b= -2 c=3 d= -4

formulae:alpha + beta +gama= -b/a

alpha beta+beta gama+gama alpha=c/a

alpha beta gama = -d/a

alpha²beta²+beta²gama²+gama²alpha²=

(alpha beta)²+(beta gama)²+(gama alpha)²

Thus (a+b+c)²=a²+b²+c²+2(ab+bc+ca)

send +2(ab+bc+ca) to LHS so we get

a²+b²+c²= (a+b+c)²-2(ab+bc+ca)

Substitute alpha beta gama in the above formula

(alpha beta)²+(beta gama)²+(gama alpha)²=

(alpha beta +beta gama+ gama alpha)²-2(alpha beta² gama + beta gama²alpha + gama alpha² beta)²

Take alpha beta and game common so it becomes

(alpha beta)²+(beta gama)²+(gama alpha)²=(alpha beta+ beta gama+ gama alpha)-2alpha beta gama(beta+alpha+gama)

formulae:alpha beta+beta gama +gama alpha=c/a

3²-2alpha beta gama(alpha+beta+gama)

9-2(4)(2)=9-16=-7