Question

if p not equals to q and p^2=5p-3 and q^2=5q-3 what is the value of p and q

Answer 1

since p^2=5p-3
and q^2=5q-3
Hence p,q are the roots of x^2=5x-3
Or, x^2-5x+3=0
Now p+q=-(-5)/1
Or, p+q=5
and pq=3/1
Or, pq=3
Now (p-q)^2=(p+q)^2-4pq
==(5)^2-4×3
=25-12=13
hence p-q=+√13,-√13
taking p-q=√13 and adding with p+q=5
we have p+q+p-q=5+√13
Or,2p=5+√13
Or, p=(5+√13)/2
And q=5-(5+√13)/2

Or,q=(5-√13)/2
taking p-q=-√13 and adding with p+q=5
we have p+q+p-q=5-√13
Or, 2p=5-√13
Or, p=(5-√13)/2
And q=5-(5-√13)/2
Or, q=(5+√13)/2

Answer 2

Step-by-step explanation:

HELLO DEAR,

GIVEN : p^2= 5p-3

q^2= 5q-3

p and q are not equal.

To find the value of p and q as per question.

SOLUTION: By solving ,p^2= 5p-3

p^2-5p+3=0

p= [-(-5)+-√{(-5)^2-4(1)(3)] /2(1)

By shridhacharya rule.

p= [5+-√{25-12}]/2

p= [5+-√(13)]/2

p=[ 5+√(13)]/2. p= [5-√(13)]/2

By solving q^2= 5q-3

q^2-5q+3=0

By shridhacharya rule

q= [-(-5)+-√{(-5)^2-4(1)(3)}]/2

q= [5+-√{25-12}]/2

q= [5+-√{13}]/2

q= [5+√{13}]/2. q= [5-√{13}]/2

Value of p and q is not equal, therefore if p= [5+√{13}]/2 then q=[5-√{13}]/2

And if p= [5-√{13}]/2 then q= [5+√{13}]/2.

I HOPE IT'S HELP YOU DEAR,

THANKS.