Question

0. Using properties of proportion, find x
(i)
√2- x /√2-x+√2+x/√2+x=3

Answer 1

Answer:

√2- x /√2-x+√2+x/√2+x=3

1 + 1 = 3

I think the question is incorrect........ it may be..........

√2- x /√2+x+√2+x/√2-x=3      

(√2- x ) (√2-x ) / (√2+x)(√2-x )  +   (√2+x ) (√2+x )  /  (√2-x)(√2+x) = 3      

{ (√2-x ) ^2 +   (√2+x ) ^2 }  / {  2 - x^2 } = 3

2 - 2√2 x + x² + 2 + 2√2 x + x² = 3 ( 2 - x² )

4 + 2 x² = 6 - 3 x²

3x² + 2x² = 6 - 4

5 x² = 2

x² = 2/5

x = ± √( 2/ 5 ) (answer )

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Answer 2

The value of x is

x = 3.

Given equation,

x 2 +x+1x 2 −x+1 = 13(x+1)14(x−1)

(1) x 2 +x+1x 2 −x+1 = 13x+1314x−14

Now, using the componendo dividendo property that is.

if ba = dc then a−ba+b = c−dc+d

We can write (1) as.

(x−27)(x 2 +1)=(−x)(27x−1)

x 3 −27x 2 +x−27=−27x 2 +x

x 3 −27x 2 +27x 2 +x−x=27

x 3 =27

therefore,

x = 3x=3