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Maths-

General

Easy

Question

A Pythagorean triple is a set of three positive integers a, b and c that satisfy $a squared plus b squared equals c squared$ . The Identity $open parentheses straight x squared minus straight y squared close parentheses squared plus left parenthesis 2 xy right parenthesis squared equals open parentheses straight x squared plus straight y squared close parentheses squared$ can be used to generate Pythagorean triples. Use the identity to generate a Pythagorean triple when x = 5 and y = 4

The correct answer is: Thus, the triplet are 3,4&5.

ANSWER:
Hint:
Pythagorean Theorem is a theorem in geometry where the square of the length of the hypotenuse of a right triangle equals the sum of the squares of the lengths of the other two sides.
We are asked to use the identity $open parentheses straight x squared minus straight y squared close parentheses squared plus left parenthesis 2 xy right parenthesis squared equals open parentheses straight x squared plus straight y squared close parentheses squared$ to find a Pythagorean triplet when x = 5 and y = 4.
Step 1 of 3:
The identity is: $open parentheses straight x squared minus straight y squared close parentheses squared plus left parenthesis 2 xy right parenthesis squared equals open parentheses straight x squared plus straight y squared close parentheses squared$
Step 2 of 3:
Substitute the values in the identity;
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell open parentheses x squared minus y squared close parentheses squared plus left parenthesis 2 x y right parenthesis squared equals open parentheses x squared plus y squared close parentheses squared end cell row cell open parentheses 5 squared minus 4 squared close parentheses squared plus open parentheses 2 cross times to the power of blank 5 cross times to the power of blank 4 close parentheses squared equals open parentheses 5 squared plus 4 squared close parentheses squared end cell row cell left parenthesis 25 minus 16 right parenthesis squared plus left parenthesis 40 right parenthesis squared equals left parenthesis 25 plus 16 right parenthesis squared space space space space space space end cell row cell 9 squared plus 1600 equals left parenthesis 41 right parenthesis to the power of 2 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space end exponent end cell row cell 81 plus 1600 equals 1681 space space space space space space space space space space space space space space space space space space space space space space space space end cell row cell 1681 equals 1681 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space end cell end table$
Step 3 of 3:
To get the Pythagorean triplet, we have:
$x equals 5 straight & y equals 4$
So,
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell y squared minus x squared equals c to the power of 2 space space space end exponent end cell row cell 5 squared minus 4 squared equals c squared space space space end cell row cell 25 minus 16 equals c squared space space space end cell row cell 9 equals c to the power of 2 space space space space space space space space space space space space space space space space space end exponent end cell row cell 3 equals c space space space space space space space space space space space space space space space end cell end table$
Thus, the triplet are 3,4&5.
Note:
Pythagorean property is an important property in right angled triangles. It helps you to find the measurements of the corresponding triangle.

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