Question
If x3 + y3 + z3 =
3(1 + xyz), P = y + z – x, Q = z + x – y and R = x + y – z, then what is the value of P3 + Q3 + R3– 3PQR?Solution
P = y + z – x, Q = z + x – y and R = x + y – z And x3 + y3 + z3 = 3(1 + xyz); Suppose x = y = 0 then z3 = 3; P = z, Q = z and R = -z; Putting these values in below equation P3 + Q3 + R3 - 3PQR = z3 + z3 - z3 + 3z3 => 4z3 Putting z3 = 3: P3 + Q3 + R3 - 3PQR = 12
In a certain code language, ‘LADDER’ is coded as '32' and ‘SOUTH’ is coded as '11'. How will ‘MOTHER’ be coded in the same coding language?<...
When all the letters of the word “PARAMETER” are written in alphabetical order from left to right, which letter is third to the left of second lette...
If in the given number 674278486, 2 is added to all the odd place digits and 1 is subtracted from the even place digits (from the left end) , then all t...
- If all the vowels of the word ‘WINTER’ are replaced by their immediate succeeding letters and all the consonants are replaced by their immediate preced...
How many pairs of letters are there in the word ‘REPLENISH, which has as many letters between them (both forward and backward) in the word as in the ...
How many pairs of letters are there in the word “POWDER” each of which has as many letters between them in the word as in alphabetical serie...
If all the alphabets of the word ‘PARALLEL’ are replaced by two succeeding letter in the alphabetical series, then what is the difference between th...
If all the digits of the number 298664321 are arranged in decreasing order, then sum of 5 th and 6 th digits (from the left end) of the number thus for...
If all the vowels in the word ‘FALSEHOOD’ are changed to the next letter in the English alphabetical order and all the consonants remain the same ...
How many pairs of letters are there in the word ‘CAPSICUM’ which has as many letters between them in the word as in the alphabetical series?
Relevant for Exams:
