Question

1) If the D of the quadratic eqn 6x²-bx+2 =0 is 1 then find b .

2) The sum of the squares of the two natural no is 52 ,If the first no is 8 less than twice the second no ,find the nos.

3) Two water taps together can fill a tank in
$3 \frac{1}{3}$
hrs .The tap of larger diameter takes 3 hrs less than the smaller one to fill the tank respectively .Find the time in which each tap can separately fill a tank.

Answer 1

this is the answer for your question.

Answer 2

Heya......

●if ax2 + bx + c = 0,
then , discriminant (D) = b2 - 4ac
1 = b2 - 4(6)(2)
1 = b2 - 48
b2 = 49
b = 7 or -7.


●There aren’t many square numbers less 52: 1, 4, 9, 16, 25, 36 and 49

if sum is 52 it isn’t hard to spot 16 = 4^2 and 36 = 6^2, the two number you are looking for are 4 and 6

If you want algebraic solution solve

a^2 + b^2 = 52 and a + 8 = 2b [where a is the first and b the second number

a = 2b - 8 substituted in first equation gives you [2b - 8]^2 + b^2 = 52, simplifies to 5b^2 - 32b + 12 = 0

(5b - 2)(b - 6) = 0

acceptable solution b = 6, and a = 4


@skb