Algebraic Formula Application : Part - 5

ALGEBRAIC FORMULA APPLICATION | MATH CHALLENGER | বীজগাণিতিক সূত্রের প্রয়োগ | Part - 5


96. $x + \frac{1}{x} = 5$ হলে, $x^6 + \frac{1}{x^6}$ = ?

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97. a = 2.234, b = 3.121, c = -5.355 হলে, $a^3 + b^3 + c^3 - 3abc$ = ?

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98. $3(a^2 + b^2 + c^2 ) = (a + b + c)^2$ হলে, a, b ও c -এর মধ্যে সম্পর্ক হল -

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99.$ {\frac{1}{2}(a - b)}^2 + ab = p(a+b)^2$ হলে, p -এর মান হল -

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100. 2x + 3y = $\frac{11}{2}$ এবং xy = $\frac{5}{6}$ হলে, $(8x^3 + 27y^3)$ = ?

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101. 999x + 888y = 1332 এবং 888x + 999y = 555 হলে, $(x^2 - y^2)$ = ?

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102. $x^2 + 4x + 3 = 0$ হলে,$ \frac{x^3}{(x^6 + 27x^3 + 27)}$ = ?

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103. k -এর মান কত হলে, $(p + \frac{1}{4}√ p + k^2)$ সংখ্যামালা পূর্ণবর্গ হবে?

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104. $\frac{x}{y} + \frac{y}{x} = -1$ (x, y ≠ 0) হলে, $x^3 - y^3$ = ?

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105.a + b + c = 4√3 এবং $a^2+b^2+c^2 = 16$ হলে, a ∶ b ∶ c = ?

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106. $(x^2 + \frac{1}{5}x + a^2)$ পূর্ণবর্গ হলে, a = ?

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107. $\frac{p^2}{q^2} + \frac{q^2}{p^2} = 1$ হলে, $p^6 + q^6$ = ?

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108. m - 5n = 2 হলে, $(m^3 - 125n^3 - 30mn)$ = ?

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109. $\frac{(6.5)^2 - (3.15)^2}{(6.5 + 3.15)}$ -এর মান কত?

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110. $(77 + \frac{1}{77})^2 - (77 - \frac{1}{77})^2$ = ?

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111. $(997)^2 + (998)^2 + (999)^2$ - 997 × 998 - 998 × 999 - 999 × 997 = ?

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112. $[(0.98)^3 + (0.02)^3 $+ 3 × (0.98) × (0.02) - 1] -এর মান হল -

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113. $ x + \frac{1}{x} = 2$ হলে, $[x^{2016} + x^{-2016}]$ -এর মান কত?

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114. x = 332, y = 333, z = 335 হলে, $x^3 + y^3 + z^3 - 3xyz$ = ?

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115. a - b = 2, $a^3 - b^3 = 26 $ হলে, $(a + b)^2 $= ?

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116. $a^3 + \frac{1}{a^3} = 2$ হলে, $\frac{(a^2 + 1)}{a} $= ?

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117. $9x^2 + 16y^2 = 60$ এবং 3x + 4y = 6 হলে, xy = ?

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118. l + m + n = 9 এবং $l^2 + m^2 + n^2 = 31$ হলে, (lm + mn + nl) = ?

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119. m + n = 1 হলে, $(m^3 + n^3 + 3mn)$ -এর মান কত ?

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