Find the value of 214-1 234-212-214-1

The correct option is C 1 ( 2^14 1 ) ( 2^34+2^12+2^14+1 ) Let 2^14=a #160;Then, the given exp =(a 1)(a^3+a^2+a+1) =(a 1)(a^2(a+1) ...

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Byju's Answer

Standard XII

Mathematics

Complex Numbers

Find the valu...

Question

Find the value of $(2^{\frac{1}{4}} - 1) (2^{\frac{3}{4}} + 2^{\frac{1}{2}} + 2^{\frac{1}{4}} + 1)$

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Solution

The correct option is C $1$
$(2^{\frac{1}{4}} - 1) (2^{\frac{3}{4}} + 2^{\frac{1}{2}} + 2^{\frac{1}{4}} + 1)$
Let $2^{\frac{1}{4}} = a$
Then, the given exp $= (a - 1) (a^{3} + a^{2} + a + 1)$
$= (a - 1) (a^{2} (a + 1) + 1 (a + 1))$
$= (a - 1) (a + 1) (a^{2} + 1)$
$= (a^{2} - 1) (a^{2} + 1)$
$= a^{4} - 1$
$∴$ Required value = ${(2^{\frac{1}{4}})}^{4} - 1 = 2 - 1 = 1$

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Find the value of $(2^{\frac{1}{4}} - 1) (2^{\frac{3}{4}} + 2^{\frac{1}{2}} + 2^{\frac{1}{4}} + 1) .$

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Find the value of (214−1)(234+212+214+1)

The correct option is C 1(214−1)(234+212+214+1)Let 214=a Then, the given exp =(a−1)(a3+a2+a+1)=(a−1)(a2(a+1)+1(a+1))=(a−1)(a+1)(a2+1)=(a2−1)(a2+1)=a4−1∴ Required value = (214)4−1=2−1=1

Find the value of $(2^{\frac{1}{4}} - 1) (2^{\frac{3}{4}} + 2^{\frac{1}{2}} + 2^{\frac{1}{4}} + 1)$