x2 + (x+5)2 = 233
2x2 + 10x + 25 = 233
2x2 + 10x - 208 = 0
2x2 + 26x - 16x - 208 = 0
2x(x+13) - 16(x+13) = 0
(2x-16)(x+13) = 0
So 2x-16 = 0 or x+13=0
So the soln is 2x-16=0 ie x = 8
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When a negative number is squared, the negative sign is essentially squared along with the number, resulting in a positive value. However, when taking the square root of a positive number, we are looking for the value that, when squared, gives us the original positive number. Since both a positive and negative number can square to the same positive value, the convention is to consider the principal (positive) square root by default. The negative square root is also a valid solution in many contexts, but for simplicity and consistency, the positive square root is typically chosen.
Usually the square of a number is greater than the original number (2x2=4, -2x-2=4) wherther the number is negative or positive. The square of 1 is the same (1x1=1) but the square of -1 is greater (-1x-1=1) The square of positive decimal numbers is smaller than the original number (0.1x0.1=0.01) and the square of negative decimal numbers is larger than the original number (-0.1x-0.1=0.01)
A composite number is a number with more than two positive integer factors (itself and one). Other than these two numbers, the positive integer factors of 155 are 5 and 31.
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The square of 9 more than a number is equal to nine more than the square of a number. What is the number?
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A prime number that is one more than a square number is known as a Sophie Germain prime. Sophie Germain primes are of the form 2p+1, where p is a prime number. For example, 17 is a Sophie Germain prime because it is one more than the square of 4, and both 4 and 17 are prime numbers. Sophie Germain primes have applications in number theory and cryptography.
more!
When a negative number is squared, the negative sign is essentially squared along with the number, resulting in a positive value. However, when taking the square root of a positive number, we are looking for the value that, when squared, gives us the original positive number. Since both a positive and negative number can square to the same positive value, the convention is to consider the principal (positive) square root by default. The negative square root is also a valid solution in many contexts, but for simplicity and consistency, the positive square root is typically chosen.
Usually the square of a number is greater than the original number (2x2=4, -2x-2=4) wherther the number is negative or positive. The square of 1 is the same (1x1=1) but the square of -1 is greater (-1x-1=1) The square of positive decimal numbers is smaller than the original number (0.1x0.1=0.01) and the square of negative decimal numbers is larger than the original number (-0.1x-0.1=0.01)
No, not always since: if a number is more than 1, then its square root is smaller than the number. if a number is less than 1, then its square root is bigger than the number.
when x is a negative number --- is a wrong answer since square root of a negative number is not defined. So x has to be zero or a positive number. The correct answer is that when x lies between 0 and 1 (with both limits excluded), its square root is greater than the number itself. Of course at both limits, the square root (assuming the positive square root - since a square root of a number can be positive or negative, both with the same absolute value) is the same as the number.
nothing it will always be positive.
(92 x 2) - (9 x 2) = 162 - 18 = 144 The number is therefore 9.