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# If t = a^2 - b^2, u = a^2 + b^2, v=2ab, what is the value of

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Joined: 19 May 2015
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If t = a^2 - b^2, u = a^2 + b^2, v=2ab, what is the value of  [#permalink]

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Updated on: 02 May 2016, 15:48
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55% (hard)

Question Stats:

65% (02:18) correct 35% (02:32) wrong based on 101 sessions

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If $$t = a^2 - b^2$$ , $$u = a^2 + b^2$$ , $$v=2ab$$ , what is the value of t, in terms of u and v?

a) $$t = \sqrt { u^2 - v^2}$$

b) $$t = \sqrt {u^2 + v^2}$$

c) $$t = \sqrt {u^2 - v}$$

d) $$t = \sqrt {u + v}$$

e) $$t = \sqrt {u^3 - v^3}$$

Originally posted by jjsverbal on 02 May 2016, 15:38.
Last edited by ENGRTOMBA2018 on 02 May 2016, 15:48, edited 2 times in total.
Reformatted the question, updated the title and added the OA.
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Joined: 02 Aug 2009
Posts: 7752
If t = a^2 - b^2, u = a^2 + b^2, v=2ab, what is the value of  [#permalink]

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02 May 2016, 22:15
mjhoon1004 wrote:
If $$t = a^2 - b^2$$ , $$u = a^2 + b^2$$ , $$v=2ab$$ , what is the value of t, in terms of u and v?

a) $$t = \sqrt { u^2 - v^2}$$

b) $$t = \sqrt {u^2 + v^2}$$

c) $$t = \sqrt {u^2 - v}$$

d) $$t = \sqrt {u + v}$$

e) $$t = \sqrt {u^3 - v^3}$$

since we have to get t in terms of u and v..
lets work on u and v..
we can easily see u and v can be converted in form of$$(a-b)^2 or (a+b)^2$$..
$$u-v = a^2+b^2-2ab = (a-b)^2$$..
and $$u+v = a^2+b^2+2ab = (a+b)^2$$..
so $$(u-v)(u+v) = {(a-b)(a+b)}^2 = (a^2-b^2)^2 = t^2$$..
or $$t = \sqrt { u^2 - v^2}$$..
ans A

another simpler method would be substitute something simple for a and b..
let a = 3 and b = 1..
so $$t = a^2-b^2 = 3^2-1^2 = 8........ u= a^2+b^2 =3^2+1^2 = 10............ v = 2ab = 2*3*1 = 6..$$

lets substitute value of u and v in all choices and see where we get t as 3..

a) $$t = \sqrt { u^2 - v^2}$$
$$t = \sqrt { 10^2 - 6^2} = 8$$.. YES

b) $$t = \sqrt {u^2 + v^2}$$
$$t = \sqrt {10^2 + 6^2} = \sqrt{136}$$.. NO

c) $$t = \sqrt {u^2 - v}$$
$$t = \sqrt {10^2 - 4} = \sqrt{96}$$

d) $$t = \sqrt {u + v}$$
$$t = \sqrt {10 + 6} = 4$$..YES

e) $$t = \sqrt {u^3 - v^3}$$
$$t = \sqrt {10^3 - 6^3} = \sqrt{784}$$.. NO

ans A
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Re: If t = a^2 - b^2, u = a^2 + b^2, v=2ab, what is the value of  [#permalink]

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07 Jan 2019, 21:53
jjsverbal wrote:
If $$t = a^2 - b^2$$ , $$u = a^2 + b^2$$ , $$v=2ab$$ , what is the value of t, in terms of u and v?

a) $$t = \sqrt { u^2 - v^2}$$

b) $$t = \sqrt {u^2 + v^2}$$

c) $$t = \sqrt {u^2 - v}$$

d) $$t = \sqrt {u + v}$$

e) $$t = \sqrt {u^3 - v^3}$$

$$(a^2 - b^2)^2$$ = $$a^4$$ + $$b^4$$ - 2$$a^2$$$$b^2$$ = $$t^2$$

$$(a^2+ b^2)^2$$ =$$a^4+b^4+2a^2b^2$$ = $$u^2$$

$$(2ab)^2 = 4a^2b^2 = v^2$$

It can be seen that $$t^2 = u^2 - v^2$$

So, t = $$\sqrt{u^2-v^2}$$

Choice A
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Re: If t = a^2 - b^2, u = a^2 + b^2, v=2ab, what is the value of  [#permalink]

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16 Jan 2019, 02:04
simply take values of a =1 and b=2 and then solve

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Re: If t = a^2 - b^2, u = a^2 + b^2, v=2ab, what is the value of   [#permalink] 16 Jan 2019, 02:04
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