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The sum of the square of a positive number and the square of 2 more than the number is 74. What is the number?

Answer 1

Julia Adams

Let the number be #x#.

#x^2+ (x + 2)^2 = 74#

#x^2 + x^2 + 4x + 4= 74#

#2x^2 + 4x - 70 = 0#

#2(x^2 + 2x - 35) = 0#

#(x + 7)(x - 5) = 0#

#x= -7 and 5#

#:.# The number is #5#.

Hopefully this helps!

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Answer 2

Ethan Adkins

Let's denote the positive number as ( x ).

According to the given information, the sum of the square of ( x ) and the square of ( 2 ) more than ( x ) is ( 74 ):

[ x^2 + (x + 2)^2 = 74 ]

Expanding and simplifying:

[ x^2 + (x^2 + 4x + 4) = 74 ] [ 2x^2 + 4x + 4 = 74 ] [ 2x^2 + 4x - 70 = 0 ]

Divide both sides by ( 2 ):

[ x^2 + 2x - 35 = 0 ]

Now, we can solve this quadratic equation. Let's factor or use the quadratic formula:

[ x^2 + 2x - 35 = (x + 7)(x - 5) = 0 ]

Setting each factor equal to zero gives us two possible solutions:

[ x + 7 = 0 \Rightarrow x = -7 \text{ (discard as we need a positive number)} ] [ x - 5 = 0 \Rightarrow x = 5 ]

So, the positive number is ( x = 5 ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.