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નિશ્વાયક

જો $open vertical bar table row bold a bold b cell bold ax bold plus bold by end cell row bold b bold c cell bold ax bold plus bold cy end cell row cell bold ax bold plus bold by end cell cell bold bx bold plus bold cy end cell bold 0 end table close vertical bar bold space bold equals bold space bold 0$ અને ax² + 2bxy + cy² ≠ 0 તો.........

a, b, cસમગુણોત્તર શ્રેણીમાં છે.
a, b, c સમાંતર શ્રેણીમાં છે.
a, b, c સ્વરિત શ્રેણીમાં છે.
a, b, c એ સમગુણોત્તર, સમાંતર કે સ્વરિત શ્રેણીમાં નથી.

જો s = p + q + r, તો $open vertical bar table row cell bold s bold plus bold r end cell bold p bold q row bold r cell bold s bold plus bold p end cell bold q row bold r bold p cell bold s bold plus bold q end cell end table close vertical bar$ ની કિંમત ....... છે.

s³
2s³
2s²
3s³

જો $bold D bold space bold equals bold space open vertical bar table row bold 1 bold 1 bold 1 row bold 1 cell bold 1 bold plus bold x end cell bold 1 row bold 1 bold 1 cell bold 1 bold plus bold y end cell end table close vertical bar$ જ્યાં x ≠ 0, y ≠ 0 તો D એ ....... x, y ∈ N

x અને y વડે વિભાજ્ય છે.
x વડે વિભાજ્ય છે પરંતુ y વડે વિભાજ્ય નથી.
x વડે વિભાજ્ય નથી પરંતુ y વડે વિભાજ્ય છે.
x અને y પૈકી એક પણ વડે વિભાજ્ય નથી.

x અને y વડે વિભાજ્ય છે.

Tips: -

$bold D bold space bold equals bold space open vertical bar table row bold 1 bold 1 bold 1 row bold 1 cell bold 1 bold plus bold x end cell bold 1 row bold 1 bold 1 cell bold 1 bold plus bold y end cell end table close vertical bar bold space bold space bold space bold space bold equals bold space open vertical bar table row bold 0 cell bold minus bold x end cell bold 0 row bold 0 bold x cell bold minus bold y end cell row bold 1 bold 1 cell bold 1 bold plus bold y end cell end table close vertical bar bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold R subscript bold 21 bold space bold left parenthesis bold minus bold 1 bold right parenthesis bold space bold space bold space bold R subscript bold 32 bold space bold space bold left parenthesis bold minus bold 1 bold right parenthesis bold space bold space bold space bold space bold space bold equals bold space bold xy$

આથી, D એ અને y વડે વિભાજ્ય છે.

જો, w એ 1 નું ઘન મૂળ હોય, અને w ≠ 1 $open vertical bar table row bold 1 cell bold 1 bold plus bold i bold plus bold w to the power of bold 2 end cell cell bold w to the power of bold 2 end cell row cell bold 1 bold minus bold i end cell cell bold minus bold 1 end cell cell bold w to the power of bold 2 bold minus bold 1 end cell row cell bold minus bold i end cell cell bold minus bold 1 bold plus bold w bold minus bold i end cell cell bold minus bold 1 end cell end table close vertical bar bold space bold equals bold space bold. bold. bold. bold. bold. bold. bold. bold. bold space$

જો 1, w, w² એ 1 નાં ઘન મુળ હોય, તો $open vertical bar table row bold 1 cell bold w to the power of bold n end cell cell bold w to the power of bold 2 bold n end exponent end cell row cell bold w to the power of bold n end cell cell bold w to the power of bold 2 bold n end exponent end cell bold 1 row cell bold w to the power of bold 2 bold n end exponent end cell bold 1 cell bold w to the power of bold n end cell end table close vertical bar bold space bold equals bold space bold. bold. bold. bold. bold. bold. bold. bold. bold. bold. bold.$

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