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SOLVE Question 6 and 7
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Answer 1

6) Solve for x: 4x^2 -2 (a^2+b^2)x + a^2b^2=0
4x^2-2 (a^2+b^2)x + a^2b^2=0
or, 4x^2 - 2a^2x - 2b^2x + a^2b^2=0
or, 2x (2x - a^2) - b^2 (2x - a^2) = 0
or, (2x - b^2) (2x - a^2) = 0

So, (2x - b^2) = 0
or, 2x = b^2
or, x = b^2/2

And, (2x - a^2)=0
or, 2x= a^2
or,x = a^2/2




7) Solve for x: 4x^2 - 4a^2x + (a^4 - b^2)

4x²-4a²x+(a⁴-b⁴)=0
or, 4x²-2{(a²+b²)+(a²-b²)}x+(a²+b²)(a²-b²)=0
or, 4x²-2(a²+b²)x-2(a²-b²)x+(a²+b²)(a²-b²)=0
or, 2x{2x-(a²+b²)}-(a²-b²){2x-(a²+b²)}=0
or, {2x-(a²+b²)}{2x-(a²-b²)}=0
Either, 2x-(a²+b²)=0
or, 2x=a²+b²
or, x=(a²+b²)/2
Or, 2x-(a²-b²)=0
or, 2x=a²-b²
or, x=(a²-b²)/2
∴ x=(a²+b²)/2, (a²-b²)/2 Ans.

Answer 2

Answer:

Metals can be easily transformed into thin sheets and thus are said to be malleable. Furthermore, metals can be converted into thin long wires hence shows ductility. Also when the metal surface is hit with great force then a ringing sound gets produced thereby showing sonorous behaviour.

As metals have generally 1, 2 or 3 electrons in the outermost shell (except hydrogen). Thus can easily donate electrons thereby forming cations. A metal easily reacts with acid and generates hydrogen gas with a popping sound.

Definition of Non-metals

Non-metals are materials that are soft and possess poor electrical and thermal conductivity. This means that non-metals restrict the flow of electric current through them. However, graphite stands here as an exception because it exhibits good electrical conductivity.