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solve this anyoneIf √2 = 1.41 and √5 = 2.24 then find value of 3/(8√2 + 5√5) + 2/(8√2 - 5√5)
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solve this anyoneIf √2 = 1.41 and √5 = 2.24 then find value of 3/(8√2 ...
Solution:
Given: √2 = 1.41 and √5 = 2.24
We need to find the value of:
3/(8√2 + 5√5) 2/(8√2 - 5√5)
Step 1: Rationalizing the denominators
We can rationalize the denominators by multiplying and dividing with the conjugates of the denominators.
For the first expression:
3/(8√2 + 5√5) = 3(8√2 - 5√5)/(64*2 - 25*5)
= 3(8√2 - 5√5)/(128 - 125)
= 3(8√2 - 5√5)/3
= 8√2 - 5√5
For the second expression:
2/(8√2 - 5√5) = 2(8√2 + 5√5)/(64*2 - 25*5)
= 2(8√2 + 5√5)/(128 - 125)
= 2(8√2 + 5√5)/3
= (16√2 + 10√5)/3
Step 2: Substituting the given values
Substituting the given values of √2 and √5, we get:
8√2 - 5√5 = 8(1.41) - 5(2.24) = -1.88
(16√2 + 10√5)/3 = (16(1.41) + 10(2.24))/3 = 6.66
Therefore, the values of the given expressions are:
3/(8√2 + 5√5) = -1.88
2/(8√2 - 5√5) = 6.66
Hence, the solution.
Given: √2 = 1.41 and √5 = 2.24
We need to find the value of:
3/(8√2 + 5√5) 2/(8√2 - 5√5)
Step 1: Rationalizing the denominators
We can rationalize the denominators by multiplying and dividing with the conjugates of the denominators.
For the first expression:
3/(8√2 + 5√5) = 3(8√2 - 5√5)/(64*2 - 25*5)
= 3(8√2 - 5√5)/(128 - 125)
= 3(8√2 - 5√5)/3
= 8√2 - 5√5
For the second expression:
2/(8√2 - 5√5) = 2(8√2 + 5√5)/(64*2 - 25*5)
= 2(8√2 + 5√5)/(128 - 125)
= 2(8√2 + 5√5)/3
= (16√2 + 10√5)/3
Step 2: Substituting the given values
Substituting the given values of √2 and √5, we get:
8√2 - 5√5 = 8(1.41) - 5(2.24) = -1.88
(16√2 + 10√5)/3 = (16(1.41) + 10(2.24))/3 = 6.66
Therefore, the values of the given expressions are:
3/(8√2 + 5√5) = -1.88
2/(8√2 - 5√5) = 6.66
Hence, the solution.
Community Answer
solve this anyoneIf √2 = 1.41 and √5 = 2.24 then find value of 3/(8√2 ...
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solve this anyoneIf √2 = 1.41 and √5 = 2.24 then find value of 3/(8√2 + 5√5) + 2/(8√2 - 5√5)
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