Find the sum of a2-2-b3-3-c3-4 - 2 a2-3-3 b3-4-4 c3-5 and a2-b3-c3-

The correct option is C 13/6a^2+25/12b^3 1/20c^3( a^2/2+b^3/3 c^3/4 )+(2a^2/3+3b^3/4 4c^3/5 )+(a^2+b^3+c^3) Grouping the like terms together, =( a^2/2+2a^2/3 ...

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Byju's Answer

Standard VII

Mathematics

Addition of Algebraic Expressions

Find the sum ...

Question

Find the sum of $\frac{a^{2}}{2} + \frac{b^{3}}{3} - \frac{c^{3}}{4}; \frac{2 a^{2}}{3} + \frac{3 b^{3}}{4} - \frac{4 c^{3}}{5}$ and $a^{2} + b^{3} + c^{3}$ .

\frac{13}{6} a - \frac{25}{12} b^{3} - \frac{12}{20} c^{3}

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\frac{13}{6} a^{2} - \frac{1}{20} b^{3} - \frac{25}{12} c^{3}

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\frac{13}{6} a^{2} + \frac{25}{12} b^{3} - \frac{1}{20} c^{3}

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\frac{13}{6} b^{3} + \frac{25}{12} a^{3} - \frac{1}{20} c^{3}

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Solution

The correct option is C $\frac{13}{6} a^{2} + \frac{25}{12} b^{3} - \frac{1}{20} c^{3}$
$(\frac{a^{2}}{2} + \frac{b^{3}}{3} - \frac{c^{3}}{4}) + (\frac{2 a^{2}}{3} + \frac{3 b^{3}}{4} - \frac{4 c^{3}}{5}) + (a^{2} + b^{3} + c^{3})$

Grouping the like terms together,
= $(\frac{a^{2}}{2} + \frac{2 a^{2}}{3} + a^{2}) + (\frac{b^{3}}{3} + \frac{3 b^{3}}{4} + b^{3}) + (\frac{- c^{3}}{4} - \frac{4 c^{3}}{5} + c^{3})$

Adding all the like terms,
= $\frac{3 a^{2} + 4 a^{2} + 6 a^{2}}{6} + \frac{4 b^{3} + 9 b^{3} + 12 b^{3}}{12} + \frac{- 5 c^{3} - 16 c^{3} + 20 c^{3}}{20}$

= $\frac{13}{6} a^{2} + \frac{25}{12} b^{3} - \frac{1}{20} c^{3}$

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Similar questions

Q. Add

\frac{a^{2}}{2} + \frac{b^{3}}{3} - \frac{c^{3}}{4}; \frac{2 a^{2}}{3} + \frac{3 b^{3}}{4} - \frac{4 c^{3}}{5}; a^{2} + b^{3} + c^{3}

Q. Addition of

\frac{a^{2}}{2} + \frac{b^{3}}{3} + \frac{c^{3}}{4}, \frac{2 a^{2}}{3} + \frac{3 b^{3}}{4} - \frac{4 c^{3}}{5}

and

a^{2} + b^{3} + c^{3}

a^{2} b^{2} c^{2} (a^{- 3} + b^{- 3} + c^{- 3}) = (a^{3} + b^{3} + c^{3})

Q. If

(a_{1}, a_{2}, a_{3})

(b_{1}, b_{2}, b_{3})

and

(c_{1}, c_{2}, c_{3})

are linearly independent and

x (a_{1}, a_{2}, a_{3}) + y (b_{1}, b_{2}, b_{3}) + z (c_{1}, c_{2}, c_{3}) = 0

then

Q. If

a + b + c = 1; a^{2} + b^{2} + c^{2} = 2; a^{3} + b^{3} + c^{3} = 3

, then

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Find the sum of a22+b33−c34;2a23+3b34−4c35 and a2+b3+c3.

The correct option is C 136a2+2512b3−120c3(a22+b33−c34)+(2a23+3b34−4c35)+(a2+b3+c3) Grouping the like terms together, =(a22+2a23+a2)+(b33+3b34+b3)+(−c34−4c35+c3) Adding all the like terms, =3a2+4a2+6a26+4b3+9b3+12b312+−5c3−16c3+20c320 = 136a2+2512b3−120c3

Find the sum of $\frac{a^{2}}{2} + \frac{b^{3}}{3} - \frac{c^{3}}{4}; \frac{2 a^{2}}{3} + \frac{3 b^{3}}{4} - \frac{4 c^{3}}{5}$ and $a^{2} + b^{3} + c^{3}$ .