Maths-
General
Easy
Question
If
find the values of ![x squared plus 1 over x squared](data:image/png;base64,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)
Hint:
Hint:
Rationalization is a technique which is used to eliminate the irrational number in the denominator.
For example,
can be rationalised as ![fraction numerator 1 over denominator square root of 3 end fraction cross times fraction numerator square root of 3 over denominator square root of 3 end fraction equals fraction numerator square root of 3 over denominator 3 end fraction](data:image/png;base64,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)
The correct answer is: 14
Given x = ![2 plus square root of 3](data:image/png;base64,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)
Step 1 of 2:
Find the value of x2
![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 x squared equals left parenthesis 2 plus square root of 3 right parenthesis squared end cell row cell x squared equals 4 plus 3 plus 2 cross times 2 cross times square root of 3 end cell row cell x squared equals 7 plus 4 square root of 3 end cell end table](data:image/png;base64,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)
Step 2 of 2:
Put the value of x2 in ![x squared plus 1 over x squared](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAD8AAAAmCAYAAABzhkOMAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAAATZJREFUeNpjYBj6QA2Ia4H4AsMIBIuBOA2I/zOMYDDq+VHPj3p+1PM0sQSEfwHxUSBWGYkxzwTEWUB8biQn+x8j1fP2QHxwJHpeEprnlQaBp9ExzdvTW6ABMKIAyMPbgJhvONXFyUDcgUW8GSoHAyCPawzHhgio2hJH4icC8RQq5rFB7XkPIO6Dsl2AeO9Ia4LuhlZhoMEBYRqUxMSmmv80xDhBAbTpqjfSOh/WQLwGmvQjR5LnQY2VTUDMBcQ8QHyGCsl+SHheFFqFIXvWhwEyPjasPc8GxOuAWBqL3HJoDTDU+vWDsctNVzDYutwDAn6MVI8Ppi433Ttgg6HLTXcw2uUeTp6iR5d7UANad7kHNaB1l3vQA2p2uYccoGWXe1ADWne5By2gR5d7UAJ6dbkHHaBZlxsAj+p48P3RLPYAAACkdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1zdXA+PG1pPng8L21pPjxtbj4yPC9tbj48L21zdXA+PG1vPis8L21vPjxtZnJhYz48bW4+MTwvbW4+PG1zdXA+PG1pPng8L21pPjxtbj4yPC9tbj48L21zdXA+PC9tZnJhYz48L21hdGg+3LqjbQAAAABJRU5ErkJggg==)
![x squared plus 1 over x squared equals 7 plus 4 square root of 3 plus fraction numerator 1 over denominator 7 plus 4 square root of 3 end fraction](data:image/png;base64,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)
Rationalizing
in the upper equation
![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 equals 7 plus 4 square root of 3 plus fraction numerator 1 over denominator 7 plus 4 square root of 3 end fraction cross times fraction numerator 7 minus 4 square root of 3 over denominator 7 minus 4 square root of 3 end fraction end cell row cell equals 7 plus 4 square root of 3 plus fraction numerator 7 minus 4 square root of 3 over denominator 49 minus 48 end fraction end cell row cell equals 7 plus 4 square root of 3 plus 7 minus 4 square root of 3 end cell row cell x squared plus 1 over x squared equals 14 end cell end table](data:image/png;base64,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)
Final Answer:
Hence, the value of
is 14
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Maths-General
Maths-
Approximate the following irrational numbers to the nearest whole number.![square root of 28](data:image/png;base64,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)
Approximate the following irrational numbers to the nearest whole number.![square root of 28](data:image/png;base64,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)
Maths-General
Maths-
A certain number of men can finish a piece of work in 100 days. If there were 10 men less, it would take 10 days more for the work to be finished. How many men were there originally?
A certain number of men can finish a piece of work in 100 days. If there were 10 men less, it would take 10 days more for the work to be finished. How many men were there originally?
Maths-General
Maths-
A flagstaff 17.5 m high casts a shadow of length 40.25 m. What is the height of the building which casts a shadow of length 28.75 m under similar conditions?
A flagstaff 17.5 m high casts a shadow of length 40.25 m. What is the height of the building which casts a shadow of length 28.75 m under similar conditions?
Maths-General
Maths-
If 11.25 m of a uniform iron rod weighs 42.75 kg, what will be the weight of 6 m of the same rod?
If 11.25 m of a uniform iron rod weighs 42.75 kg, what will be the weight of 6 m of the same rod?
Maths-General
Maths-
If the number 0.987098709 is displayed on a calculator that can only display ten digits, do we know whether it is rational or irrational? In one complete sentence explain why?
If the number 0.987098709 is displayed on a calculator that can only display ten digits, do we know whether it is rational or irrational? In one complete sentence explain why?
Maths-General
Maths-
A contractor can complete a certain piece of work in 9 days. He employed a certain number of men, but 6 of them are absent from the very first day, the rest could finish the work in 15 days. How many men were originally employed?
A contractor can complete a certain piece of work in 9 days. He employed a certain number of men, but 6 of them are absent from the very first day, the rest could finish the work in 15 days. How many men were originally employed?
Maths-General