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Inessa05 [86]
3 years ago
7

 For what value of x is the double product of the binomials x+2 and x–2 is 16 less than the sum of their squares?

Mathematics
2 answers:
solong [7]3 years ago
4 0

x = 2 + 2 - 2 = 4

hope it helps! :D

oee [108]3 years ago
4 0
\bf \begin{cases}
x+2\\\\
x-2
\end{cases}
\begin{cases}\qquad 
product\\
----------\\
(x+2)(x-2)\to x^2-4\leftarrow \textit{difference of squares anyway}\\\\
\textit{double that product}\\
----------\\
\boxed{2(x^2-4)}
\\\\\\
\textit{sum of their squares}\\
----------\\
(x+2)^2+(x-2)^2\\\\
\textit{16 less than that}\\
----------\\
\boxed{(x+2)^2+(x-2)^2-16}
\end{cases}

so.. for what values of "x", are those two expressions, equal to each other then?

well \bf 2x^2-8=x^2\underline{+2x}+4+x^2\underline{-2x}+4-16
\\\\\\
2x^2-8=2x^2+8-16\implies 
\begin{array}{llll}
2x^2-8&=&2x^2-8\\
same&=&same
\end{array}

for a system of equations, the solutions are where the graph converge, or intersect

well, in this case, the left-hand-side expression is exactly the same as the right-hand-side expression
 
so.. if you were to graph the one on the left-hand-side, it's just a parabola shifted vertically down by 8units

if you were to graph the right-hand-side expression, it will be exactly the same, just the same parabola right on top of the other, pancaked on one another

when both expressions are equal, the system has "infinite number of solutions", which is another way to say, for all values of "x", there's a solution

so.. for what values for "x" are those two expressions equal? for all values of "x"  or (-\infty,+\infty)\quad or\quad x\in \mathbb{R}, if you like an interval or set notation
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tankabanditka [31]
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60/100 / 1/5

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Hope this helps!
8 0
3 years ago
Solve 3(x+2)+5(x+2)=64
valkas [14]

Answer:

6

Step-by-step explanation:

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3x+5x+6+10=64

8x+16=64

8x=64-16

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divide both sides by 8

x=6

6 0
3 years ago
Simplify the ratio 5:90
Amanda [17]
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the ratio simplified is 1:18
4 0
3 years ago
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STatiana [176]
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Unless the dresser is made of paper, 45 grams is not enough. 45 kg though large (that's roughly 100 pounds if that's what you think in), the dresser might be found in the apartment where Sherlock Holmes lives. (The dresser is a piece of victorian furniture) it is much closer to what a modern dresser would weigh.
5 0
3 years ago
5/12 x 2/5???<br> CAN SOMEONE PLEASE ANSWER<br> 20 Point Reward!!!!
Fudgin [204]

Answer:

1/6

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Final answer:

1/6

4 0
2 years ago
Read 2 more answers
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