Question

Q4. What are the two consecutive even integers whose squares have sum 340?

(a) 12 and 10
(b)-12 and 14
(c) 12 and 14
(d) Both (b) and (c)​

Answer 1

Answer:

12 and 14

i hope it will help u...

Answer 2

Answer:

Let us consider the two consecutives even integers as 2x

and 2x+2

where x

is a positive integer.

Given that these integers sum of squares is 34. So, we have

⇒(2x)2+(2x+2)2=(340)2

We know that (a+b)2=a2+b2+2ab. By using this formula, we have

⇒4x2+4x2+4+8x=340

And hence on further simplification, we have

⇒8x2+8x+400−4=0⇒8x2+8x−336=0

Now on taking 8 common from the whole equation, we have

⇒8(x2+x−42)=0⇒x2+x−42=0

By splitting and grouping the common terms, we have

⇒x2+7x−6x−42=0⇒x(x+7)−6(x+7)=0⇒(x+7)(x−6)=0∴x=6,−7

Since, x is a positive integer we have x=6

Hence, the two consecutives even integers are 2x=2×6=12 and 2x+2=2×6+2=14.

Thus, the required values are 12, 14.