Question

if a^2=5a-3,b^2=5b-3 (a not equal to b) then

a) a+b =5,ab=3
b)a+b=-5,ab=3
c)a+b=-5,ab=-3
d)a+b= 5,ab=-3
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Answer 1

Answer:

$a^{2}$-$b^{2}$

(a+b)(a-b)=5a-3-5b+3

(a+b)(a-b)=5a-5b

(a+b)(a-b)=5(a-b)

a+b=5

Now;

$(a+b)^{2}$=$a^{2}$+$b^{2}$+2ab

=$5^{2}$=5a-3+5b-3+2ab

=25+6=5(a+b)+2ab

=19=5*5+2ab

=19-25=2ab

=-6=2ab

Hence ;

ab= -6/2

   =   -3

So,

a+b=5,ab=-3

Therefore The correct answer is Option D.

Answer 2

Answer:

Step-by-step explanation:

a^2-5a+3=0

b^2-5b+3=0

----------------------------

a^2-b^2-5a+5b=0

a^2-b^2=5a-5b

(a-b)(a+b)=5(a-b)

a+b=5

squaring on both sides

a^2+b^2+2ab=25

5a-3+5b-3+2ab=25

5(a+b)-6+2ab=25

25-6+2ab=25

2ab=6

ab=3

option(a)