Question

if the sum of the squares of three numbers of three positive numbers is 14 and the sum of their products taking two at a time is 11,find the sum of numbers
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Answer 1

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Question :-

The sum of the squares of 3 numbers is 14; while the sum of their products taken two at a time is 11. What is the sum?

Given :-

• The sum of the squares of 3 numbers is 14
• sum of their products taken two at a time is 11

To find :-

• find the numbers

step by step explanation :-

let the 3 no. be a , b , c

ATQ :-

$a^2 + b^2 + c^2 = 14$

$ab + bc + ca = 11$

${\underline{\huge{\mathbf{\color{pink}{formulae\: used :-}}}}}$

${\underline{\huge{\mathbf{\color{pink}{(a+b+c)^2 = a^2 + b^2 + c^2 +2(ab+bc+ca)}}}}}$

putting values :-

$(a+b+c)^2 = 14 + 2(11)$

$(a+b+c)^2 = 14+22$

$(a+b+c)^2 = 36$

$(a+b+c) = \sqrt {36}$

$a + b + c = 6$

Answer :-

sum of 3 no. = a + b + c = 36

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Answer 2

Answer:

Step-by-step explanation:

Let the three numbers be 2x, 3x and 4x.

$2x^{2}+3x^{2}+4x^{2}=725\\ 4x^{2}+9x^{2}+16x^{2}=725\\ 29x^2=725\\ x^2=25\\ x=5$

∴ The numbers are 10, 15 and 20.

Sum of squares is a statistical method for calculating the dispersion of data points in regression analysis. By deviating the least from the data, the sum of squares can be used to identify the function that fits the data the best. The purpose of a regression analysis is to assess how well a data series can be fitted to a function that could provide insight into the process by which the data series was created. In the world of finance, the sum of squares can be used to calculate the variation in asset values. The divergence of data points from the mean value is measured by the sum of squares.

While a smaller result shows little deviation from the mean, a bigger sum of squares suggests higher variability.

To The data points are subtracted from the mean, the differences are squared, and the sum of squares is computed.

Total, residual, and regressive sums of squares are the three types.

The sum of squares can be used by investors to assist in improving their investment decisions.

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