here alpha=a,beta=b

1)Given that a,b are the roots of the equation 2(x)^2-3x+4=0,find the equation whose roots are (a + (1/a)) and( b + (1/b))

(a and 1 are seperate)

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Given quadratic equation

`2x^2+3x+4=0` ,a and b are roots this equation. So

`a+b=(-3)/2`

`ab=4/2=2`

1.The equation whose roots are `(a+1/a) and (b+1/b)`

`(a+1/a)+(b+1/b)=(a+b)+(a+b)/(ab)`

`=(a+b)(1+1/(ab))=(-3/2)(1+2)=-9/2`

`(a+1/a)(b+1/b)=(ab+a/b+b/a+1/(ab))`

`=(ab+1/(ab)+(a^2+b^2)/(ab))`

`=(2+1/2+{(-3/2)^2-4}/2)`

`=45/8`

Thus required equation is

x^2-(sum of the roots)x+product of roots=0

x^2-(-9/2)x+45/8=0

x^2+(9/2)x+45/8=0

8x^2+36x+45=0

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