Question

ii) Their sum is - 5 and product is -36 .
--. plz answer fast​

Answer 1

Step-by-step explanation:

Let the numbers be x and y respectively. According to the question, x + y = 5 and xy = 6, and we have to find the numbers.

(1) According to the question,

x+y=5⟹x=(5−y)

And also xy=6

Plugging in x = 5 — y we get

(5−y)(y)=6⟹5y−y2=6

Here we can see we are getting an negative square of y. Therefore we should multiply both sides be (—1).

(−1)(5y−y2)=(−1)(6)

⟹−5y+y2=−6

⟹y2−5y=−6

⟹y2−5y+6=0

Now we can do the problem in two ways: by using the factor method or by using the quadratic formula.

(i) By using the factor method: Here we can see that the solutions of the equation are zeroes of the polynomial. In fact, there are always two solutions (or zeroes) for a quadratic polynomial. We have to splitt the middle term —5y in such a way that the new coefficients of y should sum up tp —5 and their product is 6. Both coefficients should be negative. Such two coefficients are —2 and —3. Therefore,

y2−5y+6=0

=y2−3y−2y+6=0

=y(y−3)−2(y−3)=0

=(y−2)(y−3)=0

=y=2,3

Thus the numbers are 2 and 3.

(ii) Another way to do is to use the quadratic formula. The formula is given by:

x=−b±b2−4ac−−−−−−−√2a

Where a = 1, b = —5 and c = 6. Putting these value in the formula we get:

x=5±25−24−−−−−−√2

x=5±12

x=42,62

x=2,3