Find the value of X if \(\frac{\sqrt{2}}{x+\sqrt{2}}=\frac{1}{x-\sqrt{2}}\)
3√2+4
3√2-4
3-2√2
4+2√2
Explanation
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Discussions (124)
Hmmm,
√2/x+2=1/x-√2
I'm gonna use substitution method,
Hope you are there with me 😊,
From The question..... let say, let√2=y,
that means anywhere you see√2, you put*y..... hope you are there?😊
Now,.... substituting,
y/x+y=1/x-y
Cross multiplying,we have......,
y(x-y)=x+y
xy-y²=x+y
Collecting like terms to factorize in respect to x,
xy-x=y+y²
x(y-1)=y+y²
Deviding both sides by (y-1)
x=y+y²/y-1
Don't forget that we are using substitution method ooo😅
It's now time to put back our√2 wherever we see*y in the above equation...... Hope you are still with me?😊
Now let go......
x=y+y²/y-1
Put y=√2
x=√2+(√2)²/√2-1
x=√2+2/√2-1
Now taking conjugate of surd,
We have,
3√2+4
Ans A
Thanks 🙌
Hope you understand 🤗
Brø.Ladalo
1st cros multiply. Colect likes term, factor out x and rationalize den d final answer is 2plus root 2 plus 2 root 2 plus 2. Add up and c ur answer
solve it just like normal equation :
2/X+2 = 1/X-2
Cross multiply
2(X-2) = X+2
X2-2 = X+2
Collect like terms
X2 – X = 2+2
X(2-1) = 2+2
Divide through by (2-1)
X = 2+1
2-1
Then you rationalize
(2+2)(2+1)
(2-1)(2+1)
2+2+22+2
2+2-2-1
X = 4+32
So simple
Mathematics is all about 99%in your thinking and 1% in your writing
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this equations should be represented in an explicit way for easy disintegration.
