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If ab = 20 –a^2*b^2, where both a and b are negative, then a^2 =

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If ab = 20 –a^2*b^2, where both a and b are negative, then a^2 = [#permalink] If ab = 20 –a^2*b^2, where both a and b are negative, then a^2 =   13 Jun 2019, 22:20
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If ab = 20 – a^2*b^2, where both a and b are negative, then a^2 =

A) 25/b^2

B) 20-b/b^2

C) 20/b^2

D) 20/b^2+b

E) 16/b^2
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E
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Re: If ab = 20 –a^2*b^2, where both a and b are negative, then a^2 = [#permalink] If ab = 20 –a^2*b^2, where both a and b are negative, then a^2 =   13 Jun 2019, 22:43
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ab= 20 -a2*b2
a2*b2 + ab -20 =0
a2*b2 + 5ab -4ab -20 =0
ab= 4 or ab= -5
Answer ab = 4
Hence
a2= 16/b2

So answer is (E)
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If ab = 20 –a^2*b^2, where both a and b are negative, then a^2 = [#permalink] If ab = 20 –a^2*b^2, where both a and b are negative, then a^2 =   17 Jun 2019, 18:08
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\(ab = 20 – (ab)^2\)

\(x = 20 – x^2\)

\(x^2 + x - 20 = 0\)

\((x + 5)(x - 4)\)

\(x1 = - 5\) ... a & b must be neg, can't be 5.

\(x2 = + 4\) .... (-2)(-2)

\(a^2 = 4\)

\(\frac{16}{a^2}=4\)

E
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Re: If ab = 20 –a^2*b^2, where both a and b are negative, then a^2 = [#permalink] If ab = 20 –a^2*b^2, where both a and b are negative, then a^2 =   09 Jul 2019, 08:40
ab + (a+b)^2 = 20

2*2 + 4*4 = 20 - meaning a,b = -2.

E: (-2)^2 = 16/(-2)^2
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Re: If ab = 20 –a^2*b^2, where both a and b are negative, then a^2 = [#permalink] If ab = 20 –a^2*b^2, where both a and b are negative, then a^2 =   28 Jul 2019, 17:08
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Arvind42
If ab = 20 – a^2*b^2, where both a and b are negative, then a^2 =

A) 25/b^2

B) 20-b/b^2

C) 20/b^2

D) 20/b^2+b

E) 16/b^2

Arvind42
If ab = 20 – a^2*b^2, where both a and b are negative, then a^2 =

A) 25/b^2

B) 20-b/b^2

C) 20/b^2

D) 20/b^2+b

E) 16/b^2

Letting x = ab, we have:

x = 20 - x^2

x^2 + x - 20 = 0

(x - 4)(x + 5) = 0

x = 4 or x = -5

Since both a and b are negative, x = ab will be positive. So x = 4 or ab = 4, and thus a^2*b^2 = 16 and a^2 = 16/b^2.

Answer: E
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Re: If ab = 20 –a^2*b^2, where both a and b are negative, then a^2 = [#permalink] If ab = 20 –a^2*b^2, where both a and b are negative, then a^2 =   26 Aug 2019, 10:13
Arvind42
If ab = 20 – a^2*b^2, where both a and b are negative, then a^2 =

A) 25/b^2

B) 20-b/b^2

C) 20/b^2

D) 20/b^2+b

E) 16/b^2

Given: ab = 20 – a^2*b^2, where both a and b are negative

Asked: a^2 =?

Let ab = t > 0

t^2 + t - 20 = 0
t^2 + 5t - 4t - 20 =0
(t-4)(t+5) = 0
t = ab = 4

a^2*b^2 = 16
a^2 = 16/b^2

IMO E
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Re: If ab = 20 a^2*b^2, where both a and b are negative, then a^2 = [#permalink] If ab = 20 –a^2*b^2, where both a and b are negative, then a^2 =   22 Nov 2023, 22:04
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Re: If ab = 20 a^2*b^2, where both a and b are negative, then a^2 = [#permalink]
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