If √2 = 1.414 and √3 = 1.732, then find the value of 4/(3√3 - 2√2) + 3/(3√3 + 2√2)
Solution:
Given, √2 = 1.414 and √3 = 1.732
We have to find the value of 4/(3√3 - 2√2) + 3/(3√3 + 2√2)
4/(3√3 - 2√2) + 3/(3√3 + 2√2) = 4(3√3 + 2√2) + 3(3√3 - 2√2) / (3√3 - 2√2)(3√3 + 2√2)
By using algebraic identity,
(a + b)(a - b) = a² - b²
(3√3 - 2√2)(3√3 + 2√2) = (3√3)² - (2√2)²
= 9(3) - 4(2)
= 27 - 8
= 19
So, (3√3 - 2√2)(3√3 + 2√2) = 19
Given, √2 = 1.414 and √3 = 1.732
3√3 = 3(1.732) = 5.196
2√2 = 2(1.414) = 2.828
(3√3 + 2√2) = 5.196 + 2.828
= 8.024
4(3√3 + 2√2) = 4(8.024)
= 32.096
(3√3 - 2√2) = 5.196 - 2.828
= 2.368
3(3√3 - 2√2) = 3(2.368)
= 7.104
So, 4(3√3 + 2√2) + 3(3√3 - 2√2) = 32.096 + 7.104
= 39.2
Now, 4/(3√3 - 2√2) + 3/(3√3 + 2√2) = 39.2/19
= 2.063
Therefore, 4/(3√3 - 2√2) + 3/(3√3 + 2√2) = 2.063
✦ Try This: If √2 = 1.414 and √3 = 1.732, then find the value of 6/(√3 - 3√2) + 7/(√3 + 3√2)
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 1
NCERT Exemplar Class 9 Maths Exercise 1.4 Problem 3
If √2 = 1.414 and √3 = 1.732, then find the value of 4/(3√3 - 2√2) + 3/(3√3 + 2√2)
Summary:
If √2 = 1.414 and √3 = 1.732, then the value of 4/(3√3 - 2√2) + 3/(3√3 + 2√2) is 2.063
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