Just Think
Evaluate:
( 3 . 5 ) 2 + 5 × 6 . 5 + ( 4 . 5 ) 2 ( 4 . 5 ) 2 − 5 × 6 . 5 + ( 3 . 5 ) 2
The answer is 0.
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9 solutions
how do you get 1? can't process it.
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oh.. tnx! got it anyway!! nice move sir! thanks!
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I am not sir if you want to know who are(sir's)-
@Sandeep Bhardwaj @DEEPANSHU GUPTA @Agnishom Chattopadhyay @Krishna Ar @Krishna Sharma @Satvik Golechha @Piyushkumar Palan @Sanjeet Raria and many others
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@U Z – I am a moderator. What does Sir mean?
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@Agnishom Chattopadhyay – A guru or a teacher
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@U Z – it doesn't always mean teacher, at times it is used to show respect
who it can solve this problem on less than 10 seconds without calculator....¡me!
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.....that was not on rsponse of Garrick
Nice solution, @megh choksi
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What was your method? @Anuj Shikarkhane
great method Megh
Numerator=(0.9x5)^2-(5x1.3x5)+(0.7x5)^2 =25(0.81-1.3+0.49) = 0
4.5 4.5-5 6.5+3.5*3.5 =20.25-32.5+12.25 =0
@Anuj Shikarkhane I just copied the title of your problem because I thought it was suitable for this problem
Try it and thank you
General formula:
(A - B) ^2 = A^2 - 2AB + B^2 So we have:
5 X 6.5 = 32.5
4.5 X 3.5 X 2 = 31.5
Need 1 less for the (5 X 6.5), so we can take 1 out from (5 X 36.5)
Now we have:
(((4.5)^2 - 31.5 + (3.5)^2 - 1)/ Original denominator
= ((4.5 -3.5)^2 -1)/ Original denominator
= ((1)^2 - 1)/ Original denominator
=0
Take the numerator -
First note that:
So from this
Since the numerator = 0, we have the whole fraction equalling 0.
I think you've made a small arithmetic error. In the second paragraph both answers should be 32.5, not 32.25.
BDMAS rule.................
1.multiple 5*6.5=32.5
2.find (4.5)^2 and (3.5)^2 which are 20.25 and 12.25 respectively
3.Solve numerator first i) numerator=0
Therefore ans is 0
x= 3.5, = ( X + 1 ) 2 − 5 ( x + 3 ) + x 2 / n o n e e d f o r m a t h = x 2 + 2 x + 1 − 5 x − 1 5 + x 2 = 2 x 2 − 3 x − 1 4 = ( x+2)(2x-7) = ( 3.5 +2) ( 7 -7) = 0= since numerator is zero answer is 0
Add and subtract 1 the numerator 4.5^{2} - 5 x 6.5 +3.5^{2}
then it becomes (4.5-3.5)^{2} -1 =1-1 =0
decimals not accepted is a loophole numerator is less than denominator(so answer can be 0 or 1) also 5^2+4^2-5*6=1 while denominator equals 61 so the obvious answer is 0
Numerator: (4.5)^2 - 5 X 6.5 + (3.5)^2 = 20.25 - 32.5 + 12.25 = 32.5 - 32.5 = 0
Since numerator = 0, fraction = 0.
={(4.5-3.5)^2-1}/{(4.5+3.5)^2+1} =0
Multiple the expression by 4 4 to eliminate the non-integer terms. ( 3 . 5 ) 2 + 5 ( 6 . 5 ) + ( 4 . 5 ) 2 ( 4 . 5 ) 2 − 5 ( 6 . 5 ) + ( 3 . 5 ) 2 ∗ 4 4 Distribute the 4's as 2's inside the squares and distribute between the two middle factors. = ( 3 . 5 ∗ 2 ) 2 + 5 ∗ 2 ( 6 . 5 ∗ 2 ) + ( 3 . 5 ∗ 2 ) 2 ( 4 . 5 ∗ 2 ) 2 − 5 ∗ 2 ( 6 . 5 ∗ 2 ) + ( 3 . 5 ∗ 2 ) 2 = ( 7 ) 2 + 1 0 ( 1 3 ) + ( 7 ) 2 ( 9 ) 2 − 1 0 ( 1 3 ) + ( 7 ) 2 Expand the squares and multiply out. = 4 9 + 1 3 0 + 8 1 8 1 − 1 3 0 + 4 9 = 2 6 0 0 = 0
Let a = 4 . 5
Therefore,
( a − 1 ) 2 + ( a + 0 . 5 ) ( a + 2 ) + ( a 2 ) ( a 2 ) − ( a + 0 . 5 ) ( a + 2 ) + ( a − 1 ) 2
Simplifying we get:
( a 2 − 2 a + 1 ) + ( a 2 + 2 . 5 a + 1 ) + ( a 2 ) a 2 − ( a 2 + 2 . 5 a + 1 ) + ( a 2 − 2 a + 1 )
The numerator can be simplified to:
( a 2 − 2 a + 1 ) + ( a 2 + 2 . 5 a + 1 ) + ( a 2 ) − 4 . 5 a + a 2
And since a = 4 . 5
Therefore: ( a 2 − 2 a + 1 ) + ( a 2 + 2 . 5 a + 1 ) + ( a 2 ) − a 2 + a 2 ( a 2 − 2 a + 1 ) + ( a 2 + 2 . 5 a + 1 ) + ( a 2 ) 0
Therefore, the expression = 0
1 − ( 3 . 5 ) 2 + 5 × 6 . 5 + ( 4 . 5 ) 2 2 × 5 × 6 . 5
= 1 − 5 × 6 . 5 3 . 5 × 3 . 5 + 1 + 5 × 6 . 5 4 . 5 × 4 . 5 2
= 1 − 1 . 3 0 . 4 9 + 1 . 3 0 . 8 1 + 1 2
= 1 − 1 + 1 2
= 0 . □