X^4 2x^2 3=0 ⇒ x^4 3x^2+x^2 3=0 ⇒ x^2(x^2 3)+1(x^2 3)=0 ⇒ (x^2 3)(x^2+1)=0 ⇒ x^2 3=0 or x^2+1=0 ⇒ x^2=3 or x^2= 1 {no real x possible} ∴ x=√(3) and ...

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Standard IX

Mathematics

Exponential Representation for Irrational Numbers

Solve:i x4-2x...

Question

Solve:

i) $x^{4} - 2 x^{2} - 3 = 0$

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Solution

$x^{4} - 2 x^{2} - 3 = 0$

$\Rightarrow x^{4} - 3 x^{2} + x^{2} - 3 = 0$

$\Rightarrow x^{2} (x^{2} - 3) + 1 (x^{2} - 3) = 0$

$\Rightarrow (x^{2} - 3) (x^{2} + 1) = 0$

$\Rightarrow x^{2} - 3 = 0 o r x^{2} + 1 = 0$

$\Rightarrow x^{2} = 3 o r x^{2} = - 1 {no real x possible}$

$∴ x = \sqrt{3} a n d - \sqrt{3} .$

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Exponential Representation for Irrational Numbers

Standard IX Mathematics

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Solve: i) x4−2x2−3=0

x4−2x2−3=0 ⇒ x4−3x2+x2−3=0 ⇒ x2(x2−3)+1(x2−3)=0 ⇒ (x2−3)(x2+1)=0 ⇒ x2−3=0 or x2+1=0 ⇒ x2=3 or x2=−1 {no real x possible} ∴ x=√3 and −√3.

Solve:

i) $x^{4} - 2 x^{2} - 3 = 0$