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The third proportional between (a^2 - b^2) and (a+ b)^2 is ?? Options: a). a b÷a-b. b). a - b ÷a b. c). (a - b)^2 ÷ a b. d). (a b)^2÷a-b Give answer with explanation.?
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The third proportional between (a^2 - b^2) and (a+ b)^2 is ?? Options:...
Given: Two numbers (a^2 - b^2) and (a b)^2
To find: The third proportional between (a^2 - b^2) and (a b)^2
Let's denote the third proportional as 'x'.
Using the property of proportionality, we can write:
(a^2 - b^2) : (a b)^2 = (a b)^2 : x
Cross multiplying, we get:
(a^2 - b^2) * x = (a b)^2 * (a b)^2
Simplifying, we have:
x = (a^2 - b^2) * (a b)^2 / (a b)^2
Now, let's simplify the expression step by step:
1. (a b)^2 / (a b)^2 = 1
The square of any non-zero number divided by itself is always 1.
Therefore, x = (a^2 - b^2) * 1
2. x = a^2 - b^2
So, the third proportional between (a^2 - b^2) and (a b)^2 is equal to a^2 - b^2.
Answer: c). (a - b)^2 ÷ a b
Explanation:
The correct option is c). (a - b)^2 ÷ a b.
The third proportional is the number that is in the same proportion to the given numbers as the second number is to the first number. In this case, we are given (a^2 - b^2) and (a b)^2.
By setting up the proportion, we can solve for the third proportional 'x'. Cross multiplying and simplifying the expression, we find that the third proportional is equal to a^2 - b^2.
Therefore, the correct option is c). (a - b)^2 ÷ a b.
To find: The third proportional between (a^2 - b^2) and (a b)^2
Let's denote the third proportional as 'x'.
Using the property of proportionality, we can write:
(a^2 - b^2) : (a b)^2 = (a b)^2 : x
Cross multiplying, we get:
(a^2 - b^2) * x = (a b)^2 * (a b)^2
Simplifying, we have:
x = (a^2 - b^2) * (a b)^2 / (a b)^2
Now, let's simplify the expression step by step:
1. (a b)^2 / (a b)^2 = 1
The square of any non-zero number divided by itself is always 1.
Therefore, x = (a^2 - b^2) * 1
2. x = a^2 - b^2
So, the third proportional between (a^2 - b^2) and (a b)^2 is equal to a^2 - b^2.
Answer: c). (a - b)^2 ÷ a b
Explanation:
The correct option is c). (a - b)^2 ÷ a b.
The third proportional is the number that is in the same proportion to the given numbers as the second number is to the first number. In this case, we are given (a^2 - b^2) and (a b)^2.
By setting up the proportion, we can solve for the third proportional 'x'. Cross multiplying and simplifying the expression, we find that the third proportional is equal to a^2 - b^2.
Therefore, the correct option is c). (a - b)^2 ÷ a b.
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The third proportional between (a^2 - b^2) and (a+ b)^2 is ?? Options: a). a b÷a-b. b). a - b ÷a b. c). (a - b)^2 ÷ a b. d). (a b)^2÷a-b Give answer with explanation.?
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