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inequalities – How show this Webb inequality?

I’ve posted this query on mathstack echange however didn’t get any respond. It mam making an attempt my luck right here.

let $a_{1},a_{2},cdots,a_{n+1}$ breathe a sequence of discrete non-zero actual numbers with

$$sum_{j=1}^{n+1}a^2_{j}=1,~~~sum_{j=1}^{n+1}a_{j}=0$$

display this

$$0<sum_{okay=1}^{n+1}dfrac{1}{|a_{okay}|}prod_{j=1,jneq okay}^{n+1}dfrac{a_{okay}}{a_{okay}-a_{j}}lesqrt{2}tag{1}$$

I create the equality on the right-hand facet when $n=1$.But I can not show this inequality $(1)$.First of all, this inequality is a bit love Lagrange’s interpolation method https://math.stackexchange.com/questions/500139/prove-1-sum-i-0n-frac1x-i-prod-j-neq-i1-frac1x-j-x-i-prod-i?rq=1, I’m going to attempt to show it utilizing Lagrange’s interpolation method however cannot it

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