find the mean proportional between 2-√3 and 26-15√3.
please answer fast.
Answers
Step-by-step explanation:
Given:-
2-√3 and 26-15√3.
To find:-
Find the mean proportional between 2-√3 and 26-15√3?
Solution:-
Given numbers = 2-√3 and 26-15√3
Method-1:-
Let the mean Proportional be X then
(2-√3):X :: X :(26-15√3)
Product of extremes = (2-√3)(26-15√3)
=> 2(26-15√3)-√3(26-15√3)
=> 52-30√3-26√3+45
= 97-56√3
Product of means = X×X = X^2
In the Proportion,
Product of means= Product of extremes
=> X^2 = 97-56√3
=> X=√[97-56√3]
=>X = √[97-2(√3×28×28)]
=>X= √(97-2√2352)
=>X =√[(49)^2+(√48)^2-2(√49)(√48)]
This is in the form of a^2-2ab+b^2
We know that
(a-b)^2 = a^2-2ab+b^2
Where a = √49 and b=√48
=>X =√[(49)^2+(√48)^2-2(√49)(√48)]
=>X √[√49-√48]^2
=> X =√49-√48
=>X = √(7×7)-√4×4×3)
=>X = 7-4√3
Method-2:-
Given numbers = 2-√3 and 26-15√3
We know that
The mean Proportional of the two numbers a and b is √(ab)
We have a =2-√3 and b=26-15√3
Mean Proportional
= √[(2-√3)(26-15√3)]
=√[97-56√3]
= √[97-2(√3×28×28)]
= √(97-2√2352)
=√[(49)^2+(√48)^2-2(√49)(√48)]
This is in the form of a^2-2ab+b^2
We know that
(a-b)^2 = a^2-2ab+b^2
Where a = √49 and b=√48
=√[(49)^2+(√48)^2-2(√49)(√48)]
= √[√49-√48]^2
=√49-√48
= √(7×7)-√4×4×3)
= 7-4√3
Answer:-
The mean proportional between 2-√3 and 26-15√3 is 7-4√3
Used formulae:-
- The mean Proportional of the two numbers a and b is √(ab)
- In the Proportion,
- Product of means= Product of extremes
- (a-b)^2 = a^2-2ab+b^2
Answer:
it is 7-4√3
Step-by-step explanation: