The number whose sum of the square of a positive number and the square of 4 more than the number is 208 is 8.
What is the number whose sum of the square of a given number is equal to 208?
Given:
- The sum of the square of a positive number and the square of 4 more than the number is 208.
Find:
Solution:
Let us consider that the number is x.
So, as per the given condition, we get;
[tex]x^{2} +(x+4)^{2}=208[/tex]
⇒ [tex]x^{2} +x^{2} +8x+16=208[/tex]
⇒ [tex]2x^{2} +8x=192[/tex]
⇒ [tex]x^{2} +4x=96[/tex]
⇒ [tex]x^{2} +4x+4=100[/tex]
⇒ [tex](x+2)^{2} =10^{2}[/tex]
⇒ x+2=10
⇒ x=10-2 = 8.
Hence, the sum of the square of a positive number and the square of 4 more than the number 208 is 8.
To learn more about the sum of squares, refer to:
https://brainly.com/question/9995303
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