The sum of two numbers is 4.5 and their product is 5. What are the two numbers? Please help me with this question. Also, could you please provide an explanation, not just the answer, so that I can learn how to solve like problems in future. Thank you!

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Answer 1 · 2018-07-02T05:34:28

#5/2=2.5, and, 2#.

Suppose that #x and y# are the reqd. nos.

Then, by what is given, we have,

# (1) : x+y=4.5=9/2, and, (2) : xy=5#.

From #(1), y=9/2-x#.

Subst.ing this #y# in #(2)#, we have, #x(9/2-x)=5, or, #

# x(9-2x)=10, i.e., 2x^2-9x+10=0#.

#:. ul(2x^2-5x)-ul(4x+10)=0#.

#:. x(2x-5)-2(2x-5)=0#.

#:. (2x-5)(x-2)=0#.

#:. x=5/2, or, x=2#.

When #x=5/2, y=9/2-x=9/2-5/2=2, and, #

when, #x=2, y=9/2-2=5/2=2.5#.

Thus, #5/2=2.5, and, 2# are the desired nos.!

Enjoy Maths.!