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RS Aggarwal Solutions Class 9 Mathematics Solutions for Factorization of Polynomials Exercise 3F in Chapter 3 - Factorization of Polynomials
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(0.85×0.85×0.85+0.15×0.15×0.15)/(0.85×0.85−0.85×0.15+0.15×0.15)= 1
Answer:
(0.85×0.85×0.85+0.15×0.15×0.15)/(0.85×0.85−0.85×0.15+0.15×0.15)= 1
Let us take 0.85 = a and 0.15 = b
So we know that LHS
=(𝑎×𝑎×𝑎+𝑏×𝑏×𝑏)/(𝑎×𝑎−𝑎×𝑏+𝑏×𝑏)
=(𝑎^3+𝑏^3)/(𝑎^2−𝑎𝑏+𝑏^2)
According to the equation,
𝑎^3 + 𝑏^3 = (𝑎 + 𝑏)(𝑎^2 − 𝑎𝑏 + 𝑏^2)
So we get,
=[(𝑎+𝑏)(𝑎^2−𝑎𝑏+𝑏^2)]/(𝑎^2−𝑎𝑏+𝑏^2)
Since (𝑎^2 − 𝑎𝑏 + 𝑏^2) is similar in numerator and denominator
We get,
= (a + b)
Now by replacing the values of a and b
= 0.85 + 0.15
= 1
= RHS
Hence proved
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