x=3+2√2 find out whether x-1/x is rational or irrational
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Answer:
the process by which green plants and some other organisms use sunlight to synthesize nutrients from carbon dioxide and water. Photosynthesis in plants generally involves the green pigment chlorophyll and generates oxygen as a by-product.
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6
Step-by-step explanation:
For simplification when finding the value of 1/x rationalize by 3−2(2)1/2 , i.e. Multiply both numerator and denominator by this. This will make the denominator one and you will get 3−2(2)1/2 this as numerator.
x=3+2(2)1/2
(1/x)=1/[3+2(2)1/2]
Now rationalize
(1/x)=1/[3+2(2)1/2]∗([3−2(2)1/2]/[3−2(2)1/2]
(1/x)=[3−2(2)1/2]/[32−2∗(21/2)2]
(1/x)=[3−2(2)1/2]/[9−8]=3−2(2)1/2
x+(1/x)=3+2(2)1/2+3−2(2)1/2=6
As 6 is rational hence x+1/x is rational
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