I- x-y3-1331II- x - y - z -0III- xy -28A- xzD- x-y-zE- x-y-z or none of the above relationship is established

The correct option is E x=y=z or none of the above relationship is establishedI. (x+y)^3=1331 ⇒ x+y=11 ⇒ y=11 x From equation III, x (11 x)=28 ⇒ 11x x^2=28 ...

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Standard XII

Mathematics

Distance Formula Using Complex Numbers

I. x+y3=1331I...

Question

I. $(x + y)^{3} = 1331$
II. $x - y + z = 0$
III. $x y = 28$

x < y = z

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x \leq y < z

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x < y > z

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x = y > z

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x = y = z

or none of the above relationship is established

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Solution

The correct option is E $x = y = z$ or none of the above relationship is established
I.
$(x + y)^{3} = 1331 \Rightarrow x + y = 11 \Rightarrow y = 11 - x$
From equation III,
$x (11 - x) = 28 \Rightarrow 11 x - x^{2} = 28 \Rightarrow x^{2} - 11 x + 28 = 0 \Rightarrow x^{2} - 7 x - 4 x + 28 = 0 \Rightarrow x (x - 7) - 4 (x - 7) = 0 \Rightarrow (x - 7) (x - 4) = 0 \Rightarrow x = 7, 4$
From equation I
$y = 4, 7$
From equation II
$7 - 4 + z = 0 \Rightarrow z = - 3 4 - 7 + z = 0 \Rightarrow z = 3$

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I. (x+y)3=1331 II. x−y+z=0 III. xy=28

I. $(x + y)^{3} = 1331$
II. $x - y + z = 0$
III. $x y = 28$