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kifflom [539]
3 years ago
10

If x and y are two positive real numbers such that x 2 +4y 2 =17 and xy =2, then find the value of x- 2y. a. 3 b. 4 c. 8 d. 9

Mathematics
1 answer:
Dafna11 [192]3 years ago
7 0

Answer: The value of x- 2y is a. \pm 3.

Step-by-step explanation:

Given:  x and y are two positive real numbers such that x^2+4y^2=17   and xy= 2 .

Consider (x-2y)^2=x^2-2(x)(2y)+(2y)^2\ \ \ [(a+b)^2=(a^2-2ab+b^2)]

=x^2-4xy+4y^2

=x^2+4y^2-4(xy)

Put  x^2+4y^2=17   and xy= 2 , we get

(x-2y)^2=17-4(2)=17-8=9

\Rightarrow\ (x-2y)^2=9

Taking square root on both sides , we get'

x-2y= \pm3

Hence, the value of x- 2y is a. \pm 3.

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