What is the value of 3^{2}+7^{2}+11^{2}+13^{2 | vedclass

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(D) To find the value of the expression $3^{2}+7^{2}+11^{2}+13^{2}+17^{2}-1^{2}-5^{2}-9^{2}-11^{2}-15^{2}$,we can group the terms using the identity $

Vedclass · Accepted Answer

$184$

Vedclass · Answer

(D) To find the value of the expression $3^{2}+7^{2}+11^{2}+13^{2}+17^{2}-1^{2}-5^{2}-9^{2}-11^{2}-15^{2}$,we can group the terms using the identity $a^{2}-b^{2}=(a-b)(a+b)$.First,observe that $11^{2}$ and $-11^{2}$ cancel each other out.The expression simplifies to: $(3^{2}-1^{2})+(7^{2}-5^{2})+(17^{2}-15^{2})-9^{2}$.Applying the identity $a^{2}-b^{2}=(a-b)(a+b)$:$(3-1)(3+1) = 2 	imes 4 = 8$$(7-5)(7+5) = 2 	imes 12 = 24$$(17-15)(17+15) = 2 	imes 32 = 64$Now,substitute these values back into the expression:$8 + 24 + 64 - 9^{2}$$= 96 - 81$$= 15$Wait,let us re-calculate the sum:$3^{2}=9, 7^{2}=49, 11^{2}=121, 13^{2}=169, 17^{2}=289$Sum of positive terms: $9+49+121+169+289 = 637$$1^{2}=1, 5^{2}=25, 9^{2}=81, 11^{2}=121, 15^{2}=225$Sum of negative terms: $1+25+81+121+225 = 453$Result: $637 - 453 = 184$.Thus,the correct option is $D$.

What is the value of $3^{2}+7^{2}+11^{2}+13^{2}+17^{2}-1^{2}-5^{2}-9^{2}-11^{2}-15^{2} ?$

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