The value of 32-42-52-24-40-30-3-4-5 is -

The correct option is A 123^2+4^2+5^2+24+40+30 can be written as 3^2 + 4^2 + 5^2 +(2×3×4) + (2×4×5) + (2×5×3) Comparing the above equation with the identity ...

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Byju's Answer

Standard VIII

Mathematics

Multiplication of Polynomials

The value of ...

Question

The value of $\frac{3^{2} + 4^{2} + 5^{2} + 24 + 40 + 30}{3 + 4 + 5}$ is :

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Solution

The correct option is A 12
$3^{2} + 4^{2} + 5^{2} + 24 + 40 + 30$ can be written as
$3^{2} + 4^{2} + 5^{2} + (2 \times 3 \times 4) + (2 \times 4 \times 5) + (2 \times 5 \times 3)$

Comparing the above equation with the identity
$(a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2 a b + 2 b c + 2 c a$ ,
we get, $(3 + 4 + 5)^{2} = 3^{2} + 4^{2} + 5^{2} + (2 \times 3 \times 4) + (2 \times 4 \times 5) + (2 \times 5 \times 3)$ .
Hence,
$\frac{3^{2} + 4^{2} + 5^{2} + 24 + 40 + 30}{3 + 4 + 5} = \frac{(3 + 4 + 5)^{2}}{(3 + 4 + 5)} = (3 + 4 + 5) = 12$

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The value of 32+42+52+24+40+303+4+5 is :

The correct option is A 12 32+42+52+24+40+30 can be written as 32+42+52+(2×3×4)+(2×4×5)+(2×5×3) Comparing the above equation with the identity (a+b+c)2=a2+b2+c2+2ab+2bc+2ca, we get, (3+4+5)2=32+42+52+(2×3×4)+(2×4×5)+(2×5×3). Hence, 32+42+52+24+40+303+4+5=(3+4+5)2(3+4+5)=(3+4+5)=12

The value of $\frac{3^{2} + 4^{2} + 5^{2} + 24 + 40 + 30}{3 + 4 + 5}$ is :