The expression $(1^{2} + 2^{2}) (3^{2} + 4^{2}) (5^{2} + 7^{2})$ equals

45^{2} + 85^{2}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

41^{2} + 87^{2}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

95^{2} + 15^{2}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

69^{2} + 67^{2}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct options are
A $45^{2} + 85^{2}$

B $41^{2} + 87^{2}$

C $95^{2} + 15^{2}$

D $69^{2} + 67^{2}$
(1+2i)(1-2i)(3+4i)(3-4i)(5+7i)(5-7i)
$= | (1 + 2 i) (3 + 4 i) (5 + 7 i) |^{2} = | (- 5 + 10 i) (5 + 7 i) |^{2}$ $= | - 25 - 70 + i (50 - 35) |^{2} = 95^{2} + 11^{2}$
$| (1 + 2 i) (3 - 4 i) (5 + 7 i) |^{2} = | (11 + 2 i) (5 + 7 i) |^{2} = | 41 + 87 i |^{2} = 42^{2} + 87^{2} | (1 + 2 i) (3 + 4 i) (5 - 7 i) |^{2} = | (- 5 + 10 i) (5 - 7 i) |^{2} | 45 + 85 i | = 45^{2} + 85^{2} | (1 + 2 i) (3 - 4 i) (5 - 7 i) |^{2} = 69^{2} + 67^{2}$

Suggest Corrections

Similar questions

\frac{- 12}{13}

- 72

Which of the following expression gives the value of "s". "s" is given as $1^{2} + 2^{2} + 3^{2} + 4^{2} + . . . . . . . . . . . . . . . . + 7^{2}$

\frac{5}{1^{2} 4^{2}} + \frac{11}{4^{2} 7^{2}} + \frac{5}{7^{2} 10^{2}} + . . . . . . \infty

\frac{3 + \sqrt{72}}{3 - \sqrt{72}}

{({\sqrt{72}}^{\sqrt{72}})}^{\sqrt{72}}

Join BYJU'S Learning Program